Vertices of a parallelogram taken in order are A, ( 2,-1,4) , B (1,0,-1) , C ( 1,2,3) and D.
Distance of the point P ( 8, 2,-12) from the plane of the parallelogram is

Options

A. `(4sqrt6)/9`
B. `(32sqrt6)/9`
C. `(16sqrt6)/9`
D. none

Answer

b

Explanation

`vecn=7hati+2hatj-hatk` is normal to the plane p ( 8,2,-12)
`|vec(AP)|=6hati+3hatj-16hatk`
Distance, `d=|(vec(AP).vecn)/(|vecn|)|`
` |(42+6+16)/(sqrt(49+4+1))|`
`64/sqrt54`
`64/(3sqrt6)= (64sqrt6)/18= (32sqrt6)/9`