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 coplanar vectors.
`therefore[p+q-r" "p-q" "q-r]`
`=(p+q-r).[(p-q)xx(q-r)]`
`=(p+q-r).[pxxq-pxxr-qxxq+qxxr]`
`=(p+q-r).[pxxq-pxxr+qxxr]" "(becauseqxxq=0)`
`=p.(pxxq)-p.(pxxr)+p.(qxxr)`
`+q.(pxxq)-q.(pxxr)+q.(qxxr)-r.(pxxq)-r.(pxxr)+r.(qxxr)`
=[p q r]-[q p r]-[r p q]
=[p q r]+[p q r]-[p q r]
=2[p q r]-[p q r]=[p q r]