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Let the pairs veca, vecb and vecc vecd e...

Let the pairs `veca, vecb and vecc vecd` each determine a plane. Then the planes are parallel if

A

`(vecaxxvecc)xx(vecbxxvecd)=vec0`

B

`(vecaxxvecc).(vecbxxvecd)=vec0`

C

`(vecaxxvecb)xx(veccxxvecd)=vec0`

D

`(vecaxxvecb).(veccxxvecd)=0`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `vecn_(1)` and `vecn_(2)` be the vectors normal to the planes determine the pairs of vector `veca,vecb` and `vecc,vecd` respectively.
Then
`vecn_(1)-vecaxxvecb` and `vecn_(2)=veccxxvecd`
If the plane are parallel then their normals are parallel.
`:.vecn_(1)xxvecn_(2)=vec0implies(vecaxxvecb)xx(veccxxvecd)=vec0`
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