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Vertices of a parallelogram taken in ord...

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

A

`(4sqrt6)/9`

B

`(32sqrt6)/9`

C

`(16sqrt6)/9`

D

none

Text Solution

Verified by Experts

The correct Answer is:
b
`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`
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