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Consider a plane x+y-z=1 and point A(1, ...

Consider a plane `x+y-z=1` and point `A(1, 2, -3)`. A line L has the equation `x=1 + 3r, y =2 -r and z=3+4r`.
The coordinate of a point B of line L such that AB is parallel to the plane is

A

`(10, -1, 15)`

B

`(-5, 4, -5)`

C

`(4, 1, 7)`

D

`(-8, 5, -9)`

Text Solution

Verified by Experts

The correct Answer is:
d
The line `(x-1)/(3)= (y-2)/(-1) = (z-3)/(4)= r`
Any point say `B-= (3r+1, 2-r, 3+4r)` (on the line L)
`vec(AB) = 3r, -r, 4r+6`
Hence,
`vec(AB)` is parallel to `x+y-z=1`
`rArr" "3r-r-4r-6=0 or r=-3`
`B` is `(-8, 5,-9)`
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