If `veca , vecb and vecc` are non- coplanar vectors and `veca xx vecc` is perpendicular to `veca xx (vecb xx vecc)` , then the value of `[ veca xx ( vecb xx vecc)] xx vecc` is equal to

Options

A. ` [veca vecb vecc] vecc`
B. `[ veca vecb vecc] vecb`
C. ` vec0`
D. `[veca vecb vecc] veca`

Answer

c

Explanation

Given that `veca, vecb and vecc` are non-coplanar, thus
` [veca vecb vecc] ne 0`
again ` veca xx (vecb xx vecc) . (veca xx vecc) =0`
`or (veca .vecc) =0`
Hence, ` veca and vecc` are perpendicular,
` veca xx (vecb xx vecc) = (veca .vecc) vecb - (veca .vecb) vecc`
` or [veca xx (vecb xx vecc)] xx vecc = vec0`