Question

If `veca, vecb, vecc` are vectors such that `[(veca, vecb, vecc)]` = 4, then `[(veca xx vecb, vecb xx vecc, vecc xx veca)]` = ______.

Options

• 16

• 64

• 4

• 8

Answer 1

If `veca, vecb, vecc` are vectors such that `[(veca, vecb, vecc)]` = 4, then `[(veca xx vecb, vecb xx vecc, vecc xx veca)]` = 16.

Explanation:

We have, `[(veca xx vecb, vecb xx vecc, vecc xx veca)]`

= `(veca  xx vecb). {(vecb xx vecc) xx (vecc xx veca)}`

= `(veca  xx vecb). {(vecm. veca)vecc - (vecm. vecc)veca)}`  ...(where `vecm = vecb xx vecc`)

= `{(veca xx vecb).vecc}.{(veca.(vecb xx vecc)}`

= `[(veca, vecb, vecc)]^2`

= 4²

= 16