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Which one of the following planes is nor...

Which one of the following planes is normal to the plane `3x+y+z=5`?

A

`x+2y+z=6`

B

`x-2y+z=6`

C

`x+2y-z=6`

D

`x-2y-z=6`

Text Solution

Verified by Experts

The correct Answer is:
D
Direction cosines of the normal to the plane
`3x+y+z=5" are " 3,1,1`
Direction cosines of the normal to the plane
`x-2y-z=6 " are " 1,-2,-1`
Sum of the product of direction cosines
`=3xx1+1xx(-2)+1xx(-1)=0`
Hence, normals to the two planes are perpendicular to each other. Therefore two planes are also perpendicular.
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