Question

E. Find the ratio in which the surface x2 + y2 + z2 = 25 divides the line
segment joining (0,1,2) and (3,4,5).​

Answer 1

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11th

Maths

Introduction to Three Dimensional Geometry

Section Formula

Find the ratio in which the...

MATHS

Find the ratio in which the YZ-plane divides the line segment formed by joining the points (−2,4,7) and (3,−5,8).

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ANSWER

Let the YZ plane divide the line segment joining points (−2,4,7) and (3,−5,8) in the ratio k:1.

Hence, by section formula, the coordinates of point of intersection are given by :

(

k+1

k(3)−2

,

k+1

k(−5)+4

,

k+1

k(8)+7

)

On the YZ plane, the x-coordinate of any point is zero.

k+1

3k−2

=0

3k−2=0

k=

3

2

Thus, the YZ plane divides the line segment formed by joining the given points in the ratio 2:3.