Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ 6) externally in the ratio 2:3 2 1 3 2 2 4 3 3 2 6 3 5 x , y ,and z= 23 23 2 3 i.e., x=-8, y=17, and z=3 Thus, the coordinates of the required point are (â€“8, 17, 3). Question 2: Given that P (3, 2, -4), Q (5, 4, -6) and R (9, 8, -10) are collinear. Find the ratio in which Q divides PR. Solution 2: Let point Q (5, 4, â€“6) divide the line segment joining points P (3, 2, â€“4) and R (9, 8, â€“10) in the ratio k:1. Therefore, by section formula, k(9) 3 k(8) 2 k( 10) 4 (5,4, 6) , , k 1 k 1 k 1 9k 3 5 k 1 9k3 5k 5 4k 2 2 1 k 4 2 Thus, point Q divides PR in the ratio 1:2. Question 3: Find the ratio in which the YZ-plane divides the line segment formed by joining the points (-2, 4, 7) and (3, -5, 8). Solution 3: Let the YZ plane divide the line segment joining points (â€“2, 4, 7) and (3, â€“5, 8) in the ratio k:1. Hence, by section formula, the coordinates of point of intersection are given by k (3) 2 ( 5) 4 (8) 7 , k , k k 1 k 1 k 1 On the YZ plane, the x-coordinate of any point is zero. 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 ______________________________________________________________________________ 3k 2 0 k 1 3k 2 0 2 k 3 Thus, the YZ plane divides the line segment formed by joining the given points in the ratio 2:3. Question 4: 1 Using section formula, show that the points A (2, â€“3, 4), B (â€“1, 2, 1) and c 0, ,2 3 are collinear. Solution 4: 1 The given points are A (2, â€“3, 4), B (â€“1, 2, 1), and c 0, ,2 3 Let P be a point that divides AB in the ratio k:1. Hence, by section formula, the coordinates of P are given by k ( 1) 2 (2) 3 (1) 4 , k , k k 1 k 1 k 1 Now, we find the value of k at which point P coincides with point C. k 2 By taking 0 ,we obtain k = 2. k 1 1 For k = 2, the coordinates of point P are 0, ,2 3 1 i.e., 0, ,2 3 is a point that divides AB externally in the ratio 2:1 and is the same as point P. Hence, points A, B, and C are collinear. Question 5: Find the coordinates of the points which trisect the line segment joining the points P (4, 2, -6) and Q (10, -16, 6). Solution 5: Let A and B be the points that trisect the line segment joining points P (4, 2, â€“6) and Q (10, â€“16, 6) Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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