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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

a. `4sqrt(26)`

B

b. `20`

C

c. `10 sqrt(13)`

D

d. none of these

Text Solution

Verified by Experts

The correct Answer is:
d
The distance of point `(1+3r, 2-r, 3+4r)` from the plane is `(|1+3r+2-r-3-4r-1|)/(sqrt(1+1+1))= (|2r+1|)/(sqrt3)= (4)/(sqrt3)`
`rArr " "r= (3)/(2), -(5)/(2)`
Hence, the points are `A((11)/(2), (1)/(2), (10)/(2)) and B ((-13)/(2), (9)/(2), (-14)/(2))`
`rArr" "AB= sqrt(292)`
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