Class XI Chapter 12 – Introduction to Three Dimensional Geometry Maths ______________________________________________________________________________ Question 6: If A and B be the points (3, 4, 5) and (-1, 3, -7), respectively, find the equation of the set of points P such that PA 2 + PB 2 = k 2 , where k is a constant. Solution 6: The coordinates of points A and B are given as (3, 4, 5) and (â€“1, 3, â€“7) respectively. Let the coordinates of point P be (x, y, z). On using distance formula, we obtain x y z 2 2 2 2 PA 3 4 5 2 2 2 x 9 6x y 16 8y z 25 10z 2 2 2 x x y y z z 6 8 10 50 x y z 2 2 2 2 PB 1 3 7 2 2 2 x x y y z z 2 6 14 59 Now, if PA 2 + PB 2 = k 2 , then 6 8 10 50 + x 2 2x y 2 6y z 2 14z 59 2 2 2 x x y y z z 2x 2y 2z 4x 14y 4z 109 k 2 2 2 2 2 2 2 2 2 x y z 2x 7y 2z k 109 2 2 2 x y z 2x 7y 2z Thus, the required equation is k 2 109 2 =k 2 2 2 2 2 k 109 x y z 2x7y 2z 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 13 – Limits and Derivatives Maths ______________________________________________________________________________ Exercise 13.1 Book Name: **NCERT** Solutions Question 1: Evaluate the Given limit: lim x 3 x 3 Solution 1: lim x 3 x 3 = 3 + 3 = 6 Question 2: 22 Evaluate the Given limit: lim x x 7 Solution 2: 22 lim x x 7 = 22 7 Question 3: Evaluate the Given limit : Solution 3: lim r x1 2 = 1 2 lim r x1 2 Question 4: 4x3 Evaluate the Given limit: lim x 1 x2 Solution 4: 4x3 lim x1 x 2 = 4 4 3 16 3 19 42 2 2 Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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