The equation of the plane which is equally inclined to the lines `(x-1)/2=y/(-2)=(z+2)/(-1)a n d=(x+3)/8=(y-4)/1=z/(-4)` and passing through the origin is/are a. `14 x-5y-7z=0` b. `2x+7y-z=0` c. `3x-4y-z=0` d. `x+2y-5z=0`

Options

A. `14x-5y-7z=0`
B. `2x+7y-z=0`
C. `3x-4y-z=0`
D. `x+2y-5z=0`

Answer

a, b

Explanation

The plane is equaly inclined to the lines. Hence, it is perpendicular to the angle bisector of the vectors
`2hati-2hatj-hatk and 8hati+hatj-4hatk`.
Vector along the angle bisectors of the vectors are
`" "(2hati-2hatj-hatk)/(3) pm (8hati+hatj-4hatk)/(9)`
or `" "(14hati-5hatj-7hatk)/(9) and (-2hati-7hatj+hatk)/(9)`
Hence, the equations of the planes are
`" "14x-5y-7z=0 or 2x+7y-z=0`