Views
9 months ago

CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 12 –

Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ Point A divides PQ in the ratio 1:2. Therefore, by section formula, the coordinates of point A are given by 1(10) 2 4 1( 16) 2 2 1(6) 2 4 , , 6, 4, 2 1 2 1 2 1 2 Point B divides PQ in the ratio 2:1. Therefore, by section formula, the coordinates of point B are given by 2(10) 14 2( 16) 12 2(6) 14 , , 8, 10,2 21 21 21 Thus, (6, –4, –2) and (8, –10, 2) are the points that trisect the line segment joining points P (4, 2, –6) and Q (10, –16, 6). Exercise Miscellaneous Question 1: Three vertices of a parallelogram ABCD are A (3, -1, 2), B (1, 2, -4) and C (-1, 1, 2). Find the coordinates of the fourth vertex. Solution 1: The three vertices of a parallelogram ABCD are given as A (3, –1, 2), B (1, 2, –4), and C (–1, 1, 2). Let the coordinates of the fourth vertex be D (x, y, z). We know that the diagonals of a parallelogram bisect each other. Therefore, in parallelogram ABCD, AC and BD bisect each other. ∴Mid-point of AC = Mid-point of BD 31 11 22 x1 y 2 z 4 , , , , 2 2 2 2 2 2 x 1 y 2 z 4 10,2 , , 2 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ x1 y 2 z 4 1, 0, and 2 2 2 2 ⇒ x = 1, y = –2, and z = 8 Thus, the coordinates of the fourth vertex are (1, –2, 8). Question 2: Find the lengths of the medians of the triangle with vertices A (0, 0, 6), B (0, 4, 0) and (6, 0, 0). Solution 2: Let AD, BE, and CF be the medians of the given triangle ABC. Since AD is the median, D is the mid-point of BC. 06 40 00 ∴Coordinates of point D = , , 2 2 2 = (3, 2, 0) 2 2 2 AD= 03 02 60 9 436 49 7 Since BE is the median, E is the mid-point of AC. 06 00 00 Coordinates of point E = , , 3,0,3 2 2 2 2 2 2 BE= 30 04 30 916 9 34 Since CF is the median, F is the mid-point of AB. 00 0 4 60 Coordinates of point F = , , 0,2,3 2 2 2 2 2 2 Length of CF = 60 02 03 36 49 49 7 Thus, the lengths of the medians of ΔABC are 7, 34 , and 7. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

  • Page 1 and 2:

    Class XI Chapter 1 - Sets Maths ___

  • Page 3 and 4:

    Class XI Chapter 1 - Sets Maths ___

  • Page 5 and 6:

    Class XI Chapter 1 - Sets Maths ___

  • Page 7 and 8:

    Class XI Chapter 1 - Sets Maths ___

  • Page 9 and 10:

    Class XI Chapter 1 - Sets Maths ___

  • Page 11 and 12:

    Class XI Chapter 1 - Sets Maths ___

  • Page 13 and 14:

    Class XI Chapter 1 - Sets Maths ___

  • Page 15 and 16:

    Class XI Chapter 1 - Sets Maths ___

  • Page 17 and 18:

    Class XI Chapter 1 - Sets Maths ___

  • Page 19 and 20:

    Class XI Chapter 1 - Sets Maths ___

  • Page 21 and 22:

    Class XI Chapter 1 - Sets Maths ___

  • Page 23 and 24:

    Class XI Chapter 1 - Sets Maths ___

  • Page 25 and 26:

    Class XI Chapter 1 - Sets Maths ___

  • Page 27 and 28:

    Class XI Chapter 1 - Sets Maths ___

  • Page 29 and 30:

    Class XI Chapter 1 - Sets Maths ___

  • Page 31 and 32:

    Class XI Chapter 1 - Sets Maths ___

  • Page 33 and 34:

    Class XI Chapter 1 - Sets Maths ___

  • Page 35 and 36:

    Class XI Chapter 1 - Sets Maths ___

  • Page 37 and 38:

    Class XI Chapter 1 - Sets Maths ___

  • Page 39 and 40:

    Class XI Chapter 1 - Sets Maths ___

  • Page 41 and 42:

    Class XI Chapter 1 - Sets Maths ___

  • Page 43 and 44:

    Class XI Chapter 2 - Relations and

  • Page 45 and 46:

    Class XI Chapter 2 - Relations and

  • Page 47 and 48:

    Class XI Chapter 2 - Relations and

  • Page 49 and 50:

    Class XI Chapter 2 - Relations and

  • Page 51 and 52:

    Class XI Chapter 2 - Relations and

  • Page 53 and 54:

    Class XI Chapter 2 - Relations and

  • Page 55 and 56:

    Class XI Chapter 2 - Relations and

  • Page 57 and 58:

    Class XI Chapter 2 - Relations and

  • Page 59 and 60:

    Class XI Chapter 2 - Relations and

  • Page 61 and 62:

    Class XI Chapter 3 - Trigonometric

  • Page 63 and 64:

    Class XI Chapter 3 - Trigonometric

  • Page 65 and 66:

    Class XI Chapter 3 - Trigonometric

  • Page 67 and 68:

    Class XI Chapter 3 - Trigonometric

  • Page 69 and 70:

    Class XI Chapter 3 - Trigonometric

  • Page 71 and 72:

    Class XI Chapter 3 - Trigonometric

  • Page 73 and 74:

    Class XI Chapter 3 - Trigonometric

  • Page 75 and 76:

    Class XI Chapter 3 - Trigonometric

  • Page 77 and 78:

    Class XI Chapter 3 - Trigonometric

  • Page 79 and 80:

    Class XI Chapter 3 - Trigonometric

  • Page 81 and 82:

    Class XI Chapter 3 - Trigonometric

  • Page 83 and 84:

    Class XI Chapter 3 - Trigonometric

  • Page 85 and 86:

    Class XI Chapter 3 - Trigonometric

  • Page 87 and 88:

    Class XI Chapter 3 - Trigonometric

  • Page 89 and 90:

    Class XI Chapter 3 - Trigonometric

  • Page 91 and 92:

    Class XI Chapter 3 - Trigonometric

  • Page 93 and 94:

    Class XI Chapter 3 - Trigonometric

  • Page 95 and 96:

    Class XI Chapter 3 - Trigonometric

  • Page 97 and 98:

    Class XI Chapter 3 - Trigonometric

  • Page 99 and 100:

    Class XI Chapter 4 - Principle of M

  • Page 101 and 102:

    Class XI Chapter 4 - Principle of M

  • Page 103 and 104:

    Class XI Chapter 4 - Principle of M

  • Page 105 and 106:

    Class XI Chapter 4 - Principle of M

  • Page 107 and 108:

    Class XI Chapter 4 - Principle of M

  • Page 109 and 110:

    Class XI Chapter 4 - Principle of M

  • Page 111 and 112:

    Class XI Chapter 4 - Principle of M

  • Page 113 and 114:

    Class XI Chapter 4 - Principle of M

  • Page 115 and 116:

    Class XI Chapter 4 - Principle of M

  • Page 117 and 118:

    Class XI Chapter 4 - Principle of M

  • Page 119 and 120:

    Class XI Chapter 4 - Principle of M

  • Page 121 and 122:

    Class XI Chapter 4 - Principle of M

  • Page 123 and 124:

    Class XI Chapter 4 - Principle of M

  • Page 125 and 126:

    Class XI Chapter 5 - Complex Number

  • Page 127 and 128:

    Class XI Chapter 5 - Complex Number

  • Page 129 and 130:

    Class XI Chapter 5 - Complex Number

  • Page 131 and 132:

    Class XI Chapter 5 - Complex Number

  • Page 133 and 134:

    Class XI Chapter 5 - Complex Number

  • Page 135 and 136:

    Class XI Chapter 5 - Complex Number

  • Page 137 and 138:

    Class XI Chapter 5 - Complex Number

  • Page 139 and 140:

    Class XI Chapter 5 - Complex Number

  • Page 141 and 142:

    Class XI Chapter 5 - Complex Number

  • Page 143 and 144:

    Class XI Chapter 5 - Complex Number

  • Page 145 and 146:

    Class XI Chapter 5 - Complex Number

  • Page 147 and 148:

    Class XI Chapter 5 - Complex Number

  • Page 149 and 150:

    Class XI Chapter 5 - Complex Number

  • Page 151 and 152:

    Class XI Chapter 5 - Complex Number

  • Page 153 and 154:

    Class XI Chapter 5 - Complex Number

  • Page 155 and 156:

    Class XI Chapter 6 - Linear Inequal

  • Page 157 and 158:

    Class XI Chapter 6 - Linear Inequal

  • Page 159 and 160:

    Class XI Chapter 6 - Linear Inequal

  • Page 161 and 162:

    Class XI Chapter 6 - Linear Inequal

  • Page 163 and 164:

    Class XI Chapter 6 - Linear Inequal

  • Page 165 and 166:

    Class XI Chapter 6 - Linear Inequal

  • Page 167 and 168:

    Class XI Chapter 6 - Linear Inequal

  • Page 169 and 170:

    Class XI Chapter 6 - Linear Inequal

  • Page 171 and 172:

    Class XI Chapter 6 - Linear Inequal

  • Page 173 and 174:

    Class XI Chapter 6 - Linear Inequal

  • Page 175 and 176:

    Class XI Chapter 6 - Linear Inequal

  • Page 177 and 178:

    Class XI Chapter 6 - Linear Inequal

  • Page 179 and 180:

    Class XI Chapter 6 - Linear Inequal

  • Page 181 and 182:

    Class XI Chapter 6 - Linear Inequal

  • Page 183 and 184:

    Class XI Chapter 6 - Linear Inequal

  • Page 185 and 186:

    Class XI Chapter 6 - Linear Inequal

  • Page 187 and 188:

    Class XI Chapter 6 - Linear Inequal

  • Page 189 and 190:

    Class XI Chapter 6 - Linear Inequal

  • Page 191 and 192:

    Class XI Chapter 6 - Linear Inequal

  • Page 193 and 194:

    Class XI Chapter 6 - Linear Inequal

  • Page 195 and 196:

    Class XI Chapter 6 - Linear Inequal

  • Page 197 and 198:

    Class XI Chapter 7 - Permutation an

  • Page 199 and 200:

    Class XI Chapter 7 - Permutation an

  • Page 201 and 202:

    Class XI Chapter 7 - Permutation an

  • Page 203 and 204:

    Class XI Chapter 7 - Permutation an

  • Page 205 and 206:

    Class XI Chapter 7 - Permutation an

  • Page 207 and 208:

    Class XI Chapter 7 - Permutation an

  • Page 209 and 210:

    Class XI Chapter 7 - Permutation an

  • Page 211 and 212:

    Class XI Chapter 7 - Permutation an

  • Page 213 and 214:

    Class XI Chapter 7 - Permutation an

  • Page 215 and 216:

    Class XI Chapter 7 - Permutation an

  • Page 217 and 218:

    Class XI Chapter 7 - Permutation an

  • Page 219 and 220:

    Class XI Chapter 8 - Binomial Theor

  • Page 221 and 222:

    Class XI Chapter 8 - Binomial Theor

  • Page 223 and 224:

    Class XI Chapter 8 - Binomial Theor

  • Page 225 and 226:

    Class XI Chapter 8 - Binomial Theor

  • Page 227 and 228:

    Class XI Chapter 8 - Binomial Theor

  • Page 229 and 230:

    Class XI Chapter 8 - Binomial Theor

  • Page 231 and 232:

    Class XI Chapter 8 - Binomial Theor

  • Page 233 and 234:

    Class XI Chapter 8 - Binomial Theor

  • Page 235 and 236:

    Class XI Chapter 8 - Binomial Theor

  • Page 237 and 238:

    Class XI Chapter 8 - Binomial Theor

  • Page 239 and 240:

    Class XI Chapter 8 - Binomial Theor

  • Page 241 and 242:

    Class XI Chapter 9 - Sequences and

  • Page 243 and 244:

    Class XI Chapter 9 - Sequences and

  • Page 245 and 246:

    Class XI Chapter 9 - Sequences and

  • Page 247 and 248:

    Class XI Chapter 9 - Sequences and

  • Page 249 and 250:

    Class XI Chapter 9 - Sequences and

  • Page 251 and 252:

    Class XI Chapter 9 - Sequences and

  • Page 253 and 254:

    Class XI Chapter 9 - Sequences and

  • Page 255 and 256:

    Class XI Chapter 9 - Sequences and

  • Page 257 and 258:

    Class XI Chapter 9 - Sequences and

  • Page 259 and 260:

    Class XI Chapter 9 - Sequences and

  • Page 261 and 262:

    Class XI Chapter 9 - Sequences and

  • Page 263 and 264:

    Class XI Chapter 9 - Sequences and

  • Page 265 and 266:

    Class XI Chapter 9 - Sequences and

  • Page 267 and 268:

    Class XI Chapter 9 - Sequences and

  • Page 269 and 270:

    Class XI Chapter 9 - Sequences and

  • Page 271 and 272:

    Class XI Chapter 9 - Sequences and

  • Page 273 and 274:

    Class XI Chapter 9 - Sequences and

  • Page 275 and 276:

    Class XI Chapter 9 - Sequences and

  • Page 277 and 278:

    Class XI Chapter 9 - Sequences and

  • Page 279 and 280:

    Class XI Chapter 9 - Sequences and

  • Page 281 and 282:

    Class XI Chapter 9 - Sequences and

  • Page 283 and 284:

    Class XI Chapter 9 - Sequences and

  • Page 285 and 286:

    Class XI Chapter 9 - Sequences and

  • Page 287 and 288:

    Class XI Chapter 9 - Sequences and

  • Page 289 and 290:

    Class XI Chapter 9 - Sequences and

  • Page 291 and 292:

    Class XI Chapter 9 - Sequences and

  • Page 293 and 294:

    Class XI Chapter 9 - Sequences and

  • Page 295 and 296:

    Class XI Chapter 9 - Sequences and

  • Page 297 and 298:

    Class XI Chapter 9 - Sequences and

  • Page 299 and 300:

    Class XI Chapter 9 - Sequences and

  • Page 301 and 302:

    Class XI Chapter 9 - Sequences and

  • Page 303 and 304:

    Class XI Chapter 9 - Sequences and

  • Page 305 and 306:

    Class XI Chapter 9 - Sequences and

  • Page 307 and 308:

    Class XI Chapter 9 - Sequences and

  • Page 309 and 310:

    Class XI Chapter 9 - Sequences and

  • Page 311 and 312:

    Class XI Chapter 9 - Sequences and

  • Page 313 and 314:

    Class XI Chapter 10 - Straight Line

  • Page 315 and 316:

    Class XI Chapter 10 - Straight Line

  • Page 317 and 318:

    Class XI Chapter 10 - Straight Line

  • Page 319 and 320:

    Class XI Chapter 10 - Straight Line

  • Page 321 and 322:

    Class XI Chapter 10 - Straight Line

  • Page 323 and 324:

    Class XI Chapter 10 - Straight Line

  • Page 325 and 326:

    Class XI Chapter 10 - Straight Line

  • Page 327 and 328:

    Class XI Chapter 10 - Straight Line

  • Page 329 and 330:

    Class XI Chapter 10 - Straight Line

  • Page 331 and 332:

    Class XI Chapter 10 - Straight Line

  • Page 333 and 334:

    Class XI Chapter 10 - Straight Line

  • Page 335 and 336:

    Class XI Chapter 10 - Straight Line

  • Page 337 and 338:

    Class XI Chapter 10 - Straight Line

  • Page 339 and 340:

    Class XI Chapter 10 - Straight Line

  • Page 341 and 342:

    Class XI Chapter 10 - Straight Line

  • Page 343 and 344:

    Class XI Chapter 10 - Straight Line

  • Page 345 and 346:

    Class XI Chapter 10 - Straight Line

  • Page 347 and 348:

    Class XI Chapter 10 - Straight Line

  • Page 349 and 350:

    Class XI Chapter 10 - Straight Line

  • Page 351 and 352:

    Class XI Chapter 10 - Straight Line

  • Page 353 and 354:

    Class XI Chapter 10 - Straight Line

  • Page 355 and 356:

    Class XI Chapter 10 - Straight Line

  • Page 357 and 358:

    Class XI Chapter 10 - Straight Line

  • Page 359 and 360:

    Class XI Chapter 10 - Straight Line

  • Page 361 and 362:

    Class XI Chapter 10 - Straight Line

  • Page 363 and 364:

    Class XI Chapter 10 - Straight Line

  • Page 365 and 366:

    Class XI Chapter 10 - Straight Line

  • Page 367 and 368:

    Class XI Chapter 10 - Straight Line

  • Page 369 and 370:

    Class XI Chapter 10 - Straight Line

  • Page 371 and 372:

    Class XI Chapter 10 - Straight Line

  • Page 373 and 374:

    Class XI Chapter 11 - Conic Section

  • Page 375 and 376: Class XI Chapter 11 - Conic Section
  • Page 377 and 378: Class XI Chapter 11 - Conic Section
  • Page 379 and 380: Class XI Chapter 11 - Conic Section
  • Page 381 and 382: Class XI Chapter 11 - Conic Section
  • Page 383 and 384: Class XI Chapter 11 - Conic Section
  • Page 385 and 386: Class XI Chapter 11 - Conic Section
  • Page 387 and 388: Class XI Chapter 11 - Conic Section
  • Page 389 and 390: Class XI Chapter 11 - Conic Section
  • Page 391 and 392: Class XI Chapter 11 - Conic Section
  • Page 393 and 394: Class XI Chapter 11 - Conic Section
  • Page 395 and 396: Class XI Chapter 11 - Conic Section
  • Page 397 and 398: Class XI Chapter 11 - Conic Section
  • Page 399 and 400: Class XI Chapter 11 - Conic Section
  • Page 401 and 402: Class XI Chapter 11 - Conic Section
  • Page 403 and 404: Class XI Chapter 11 - Conic Section
  • Page 405 and 406: Class XI Chapter 11 - Conic Section
  • Page 407 and 408: Class XI Chapter 11 - Conic Section
  • Page 409 and 410: Class XI Chapter 11 - Conic Section
  • Page 411 and 412: Class XI Chapter 11 - Conic Section
  • Page 413 and 414: Class XI Chapter 11 - Conic Section
  • Page 415 and 416: Class XI Chapter 11 - Conic Section
  • Page 417 and 418: Class XI Chapter 12 - Introduction
  • Page 419 and 420: Class XI Chapter 12 - Introduction
  • Page 421 and 422: Class XI Chapter 12 - Introduction
  • Page 423 and 424: Class XI Chapter 12 - Introduction
  • Page 425: Class XI Chapter 12 - Introduction
  • Page 429 and 430: Class XI Chapter 12 - Introduction
  • Page 431 and 432: Class XI Chapter 13 - Limits and De
  • Page 433 and 434: Class XI Chapter 13 - Limits and De
  • Page 435 and 436: Class XI Chapter 13 - Limits and De
  • Page 437 and 438: Class XI Chapter 13 - Limits and De
  • Page 439 and 440: Class XI Chapter 13 - Limits and De
  • Page 441 and 442: Class XI Chapter 13 - Limits and De
  • Page 443 and 444: Class XI Chapter 13 - Limits and De
  • Page 445 and 446: Class XI Chapter 13 - Limits and De
  • Page 447 and 448: Class XI Chapter 13 - Limits and De
  • Page 449 and 450: Class XI Chapter 13 - Limits and De
  • Page 451 and 452: Class XI Chapter 13 - Limits and De
  • Page 453 and 454: Class XI Chapter 13 - Limits and De
  • Page 455 and 456: Class XI Chapter 13 - Limits and De
  • Page 457 and 458: Class XI Chapter 13 - Limits and De
  • Page 459 and 460: Class XI Chapter 13 - Limits and De
  • Page 461 and 462: Class XI Chapter 13 - Limits and De
  • Page 463 and 464: Class XI Chapter 13 - Limits and De
  • Page 465 and 466: Class XI Chapter 13 - Limits and De
  • Page 467 and 468: Class XI Chapter 13 - Limits and De
  • Page 469 and 470: Class XI Chapter 13 - Limits and De
  • Page 471 and 472: Class XI Chapter 13 - Limits and De
  • Page 473 and 474: Class XI Chapter 13 - Limits and De
  • Page 475 and 476: Class XI Chapter 13 - Limits and De
  • Page 477 and 478:

    Class XI Chapter 13 - Limits and De

  • Page 479 and 480:

    Class XI Chapter 13 - Limits and De

  • Page 481 and 482:

    Class XI Chapter 13 - Limits and De

  • Page 483 and 484:

    Class XI Chapter 13 - Limits and De

  • Page 485 and 486:

    Class XI Chapter 13 - Limits and De

  • Page 487 and 488:

    Class XI Chapter 13 - Limits and De

  • Page 489 and 490:

    Class XI Chapter 13 - Limits and De

  • Page 491 and 492:

    Class XI Chapter 14 - Mathematical

  • Page 493 and 494:

    Class XI Chapter 14 - Mathematical

  • Page 495 and 496:

    Class XI Chapter 14 - Mathematical

  • Page 497 and 498:

    Class XI Chapter 14 - Mathematical

  • Page 499 and 500:

    Class XI Chapter 14 - Mathematical

  • Page 501 and 502:

    Class XI Chapter 14 - Mathematical

  • Page 503 and 504:

    Class XI Chapter 14 - Mathematical

  • Page 505 and 506:

    Class XI Chapter 14 - Mathematical

  • Page 507 and 508:

    Class XI Chapter 15 - Statistics Ma

  • Page 509 and 510:

    Class XI Chapter 15 - Statistics Ma

  • Page 511 and 512:

    Class XI Chapter 15 - Statistics Ma

  • Page 513 and 514:

    Class XI Chapter 15 - Statistics Ma

  • Page 515 and 516:

    Class XI Chapter 15 - Statistics Ma

  • Page 517 and 518:

    Class XI Chapter 15 - Statistics Ma

  • Page 519 and 520:

    Class XI Chapter 15 - Statistics Ma

  • Page 521 and 522:

    Class XI Chapter 15 - Statistics Ma

  • Page 523 and 524:

    Class XI Chapter 15 - Statistics Ma

  • Page 525 and 526:

    Class XI Chapter 15 - Statistics Ma

  • Page 527 and 528:

    Class XI Chapter 15 - Statistics Ma

  • Page 529 and 530:

    Class XI Chapter 15 - Statistics Ma

  • Page 531 and 532:

    Class XI Chapter 15 - Statistics Ma

  • Page 533 and 534:

    Class XI Chapter 15 - Statistics Ma

  • Page 535:

    Class XI Chapter 15 - Statistics Ma

Untitled
Maths on track! - STEPS | Engineers Ireland
103 Trigonometry Problems
The Philosophical magazine; a journal of theoretical ... - Index of
Advanced Engineering Mathematics 10th Edition
THE MATHS TEACHER'S HANDBOOK - Arvind Gupta
View report - eResearch SA
March 2011 - Career Point
Teaching & Learning Plans - Project Maths
PDF file
t - Eötvös Loránd University
Bukhovtsev-et-al-Problems-in-Elementary-Physics
ICfJff' - Al Kossow's Bitsavers
basic_engineering_mathematics0
MARYLAND Orbital Maneuvering
Stability Of Solitary Waves Of A Generalized Two-Component ...
IIT-JEE 2010 - Career Point
Original - University of Toronto Libraries
XT – MATHS Grade 11 – Equations
The Cubic Spline - STEM2
Elliptic variational problems with critical exponent
SOME ELEMENTARY INEQUALITIES IN GAS DYNAMICS EQUATION
Optimal Bounds on the Kuramoto-Sivashinsky Equation Felix Otto ...
A Nonlinear Heat Equation with Temperature-Dependent ... - UFRJ
Convergence to Stochastic Integrals involving Non-linear Functions
Rudin's Principles of Mathematical Analysis: Solutions to ... - MIT
Read full issue - Canadian Mathematical Society
Einstein's 1905 paper
on the effect of period lengths on dynamic stability of thin biperiodic ...