Find the equation of the plane through the point (1,4,-2) and parallel to the plane `-2x+y-3z=7`.

Options

A. `2x-y+3z=8`
B. `2x-y+3z+8=0`
C. `2x-y+3z=4`
D. none of these

Answer

B

Explanation

Let the equation of a plane parallel to the plane `-2x+y-3z=7` be
`-2x+y-3z+k=0`……………i
This passes through (1,4,-2)
`:.(-2)(1)+4-3(-2)+k=0=k=-8`
Putting `k=-8` in i we obtain
`-2x+y-3z-8=0implies2x-y+3z+8=0`