Question

Let the vectors `veca, vecb,vecc and vecd` be such that `(vecaxxvecb)xx(veccxxvecd)=vec0`. Let `P_1 and P_2` be planes determined by pairs of vectors `veca,vecb and vecc,vecd respectively. Then the angle between `P_1 and P_2` is (A) 0 (B) `pi/4` (C) `pi/3` (D) `pi/2`

Answer 1

Correct Answer - a
Given that `veca. Vecb , vecc and vecd` are vectors such that
`( veca xx vecb) xx (vecc xx vecd)= vec0`
` P_(1)` is the plane determined by vectors `veca and vecb` therefore, normal vectors `vecn_(1) " to" P_(1)` will be given by
`vecn_(1) = veca xx vecb`
Similarly. `P_(2)` is the plane determined by vectors `vecc and vecd`. therefore, normal vectors `vecn_(1) " to " P_(2)` will be given by
`vecn_(2) = veca xx vecb`
Substituting the values of `vecn_(1) and vecn_(2)` in (i), we get
`vecn_(1) xx vecn_(2) = vec0`
Hence ` vecn_(1) ||vecn_(2)`
Hence, the planes will also be parallel to each other. thus angle between the planes is 0.