Let `veca vecb and vecc` be non- zero vectors aned `vecV_(1) =veca xx (vecb xx vecc) and vecV_(2) = (veca xx vecb) xx vecc`.vectors `vecV_(1) and vecV_(2)` are equal . Then

Options

A. `veca and vecb` ar orthogonal
B. `veca and vecc` are collinear
C. `vecb and vecc` ar orthogonal
D. `vecb= lambda (veca xx vecc) " when " lambda ` is a scalar

Answer

b,d

Explanation

`vecV_(1) = vecV_(2)`
`vecaxx (vecbxxvecc) = (vecaxxvecb)xxvecc`
`or (veca.vecc)vecb - (veca.vecb)vecc= (veca.vecc)vecb- (vecb.vecc)veca`
`or (veca .vecb)vecc = (vecb.vecc)veca`
Thus , either `vecc and veca` ar collinear or `vecb` is perpendicular to both `veca and vecc Rightarrow vecb = lamda (veca xx vecc) `