Question

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).

Class X1 - Maths -Introduction to Three Dimensional Geometry Page 277

Answer 1

Let A ≡ ( -2, 4 , 7 ) and B ≡ ( 3 , -5, 8 )
Now, A/C to question,
Let K : 1 ratio in YZ plane divides line AB .
But we know, in YZ plane co-ordinate of X will be zero .
So, use section formula for x - co-ordinate

x = (mx₂ + nx₁)/( m + n)
0 = (mx₂ + nx₁ )/( m + n)
mx₂ + nx₁ = 0
Now, put m = k and n = 1 also x₂ = 3 and x₁ = -2
∴ k × 3 + 1 × -2 = 0
3k -2 = 0
k = 2/3

Hence, YZ -plane divides the segment internally in the ratio 2 : 3