Find the plane passing through `(4,-1,2)` and parallel to the lines `(x+2)/3=(y-2)/(-1)=(z+1)/2a n d(x-2)/1=(y-3)/2=(z-4)/3`

Options

A. (1, 1, – 1)
B. (–1, – 1, – 1)
C. (–1, – 1, 1)
D. (1, 1, 1)

Answer

D

Explanation

Normal vector of plane
`abs({:(hati,hatj,hatk),(3,-1,2),(1,2,3):})`
`=-7hati-7hatj+7hatk`
Let equation of plane be `x+y+z=alpha`
Since it passes through `(4,-1,2)`
`alpha=1`
or `x+y-z=1` Passes through (1, 1, 1)