Correct Answer – 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)`

Correct Answer – 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)`

Correct Answer – b
The equation of plane containing the line L is
`” “A(x-1)+ B(y-2) + C(z-3)=0`,
where `3A-B+4C=0″ “` (i)
(i) also contains point `A(1, 2, -3)`.
Hence, C =0 and `3A= B`.
The equation of plane is `x-1+ 3(y-2) =0 or x+ 3y-7=0`