Question

If the three planes `x=5,2x-5ay+3z-2=0` and `3bx+y-3z=0` contain a common line, then `(a,b)` is equal to
A. `(-1/5,8/15)`
B. `(1/5,-8/15)`
C. `(-8/15,1/5)`
D. `(8/15,-1/5)`

Answer 1

Correct Answer - B
The line of intersection of first two planes is
`(x-5)/0=y/(-3)=(z+7//3)/(-5a)`
It must lie on third plane.
`:.3bxx0(-3)xx1+(-3)(-5a)=0`
and `3bxx5+0xx1+(-3)(-8//3)=0`
`impliesa=1/5` and `15b+8impliesa=1/5`and `b=-8/15`