Let vectors ` vec a , vec b , vec c ,a n d vec d` be such that `( vec axx vec b)xx( vec cxx vec d)=0.` Let `P_1a n dP_2` be planes determined by the pair of vectors ` vec a , vec b ,a n d vec c , vec d ,` respectively. Then the angle between `P_1a n dP_2` is `0` b. `pi//4` c. `pi//3` d. `pi//2`

Options

A. 0
B. `pi//4`
C. `pi//3`
D. `pi//2`

Answer

a

Explanation

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.