If p,q and r are non-zero, non-coplanar vectors then [p+q-r p-q q-r]= . . .

Options

A. 3[p q r]
B. 0
C. [p q r]
D. 2[p q r]

Answer

C

Explanation

Given, p, q and r are non-zero coplaner vectors.
`therefore[p+q-r p-qq-r]`
`=(p+q-r)dot[(p-q)xx(q-r)]`
`=(p+q-r)dot[pxxq-pxxr-qxxq+qxxr]`
`=(p+q-r).[pxxq-pxxr+qxxr](becauseqxxq=0)`
`=p.(pxxq)-p.(pxxr)+pdot(qxxr)+qdot(pxxq)-rdot(pxxq)-rdot(pxxr)+rdot(qxxr)`
`=[pqr]-[qpr]-[rpq]`
`=[pqr]+[pqr]-[pqr]`
`=2[pqr]-[pqr]=[pqr]`