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If vec P and vec Q are two vectors, then...

If `vec P and vec Q` are two vectors, then the value of `(vec P + vec Q) xx (vec P - vec Q)` is

A

`vec P xx vec Q`

B

`-(vec P xx vec Q)`

C

`2(vec Q xx vec P)`

D

`+2(vec P xx vec Q)`

Text Solution

Verified by Experts

The correct Answer is:
C
`(vec P + vec Q) xx (vec P - vec Q)`
`=vec P xx vec P -vec P xx vec Q + vec Q xx vec P -vec Q xx vec Q`
But `vec P xx vec P = vec Q xx vec Q =0 and vec P xx vec Q =- vec Q xx vec P`
`therefore (vec P + vec Q) xx (vec P - vec Q)`
`=0+vec Q xx vec P + vec Q xx vec P-0`
`=2 (vec Q xx vec P)`
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