Find the co-ordinates of a point where the line `(x-1)/(-2) = (y-2)/(3) = (z+5)/(-4)`, meets the plane `2x+4-z=3`.

Options

A. `(-3,-1,-1)`
B. `(3,1,1)`
C. `(2,-3,-1)`
D. `(3,-1,-1)`

Answer

D

Explanation

Let `(x-1)/(-2) = (y-2)/(3) = (z+5)/(-4) = lambda`
Co-ordinates of any point A on this line
`A(-2lambda+1,3lambda+2,-4lambda-5)`
This point lies on the plane `2x+4y-z=3`
`2(-2lambda+1)+4(3lambda+2)-(-4lambda-5)=3`
`rArr -4lambda+2+12lambda+8+4lambda+5=3`
`rArr 12lambda = -12`
`rArr lambda = - 1`
`:.` Co-ordinates of point `A = (3,-1,-1)`.