The line passing through the points `(1, 2, -1)` and `(3, -1, 2)` meets the yz-plane at which one of the following points? (A) `(0, -7/2, 5/2)` (B) `(0, 7/2 , 1/2)` (C) `(0, -7/2, -5/2)` (D) `(0, 7/2 , -5/2)`

Options

A. `(0,-7/2,5/2)`
B. `(0,7/2,1/2)`
C. `(0,-7/2,5/2)`
D. `(0,7/2,-5/2)`

Answer

D

Explanation

Eqn. of line
` rArr (x-x_1)/(x_2-x_1)=(y-y_1)/(y_2-y_1)=(z-z_1)/(z_2-z_1)`
`i.e, (x-1)/2=(y-2)/(-3)=(z+1)/3=K` (say)
`rArr x-1=2K, y-2=-3K,z+1=3K`
`rArr x=2K+1,y=-3K+2,z=3K-1`
Since the line meets yz plane, x=0
`:. 2K+1=0rArrK=(-1)/2`
`:. y=-3((-1)/2)+2=3/2+2=7/2`
`z=3((-1)/2)-1=(-3)/2-1=(-5)/2`