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If bar u,bar v,bar w are three non copl...

If `bar u,bar v,bar w` are three non coplanar vectors then `(bar u+bar v-bar w).{(bar u-bar v) xx (bar v-bar w)}=`

A

0

B

`u*(vxxw)`

C

`u*(wxxv)`

D

`3u*(vxxw)`

Text Solution

Verified by Experts

The correct Answer is:
B
`(u+v-w).(uxxv-uxxw-vxxv+vxxw)`
`=(u+v-w).(uxxv-uxxw+vxxw)" "[becausevxxv=0]`
`=u.(uxxv)-u.(uxxw)+u.(vxxw)+v.(uxxv)`
`-v.(uxxw)+v.(vxxw)`
`-w.(uxxv)+w.(uxxw)-w.(vxxw)`
`=u.(vxxw)-v.(uxxw)-w.(uxxv)`
`=["u v w"]+["v u w"]-["w u v"]=u.(vxxw)`
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