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Given that veca=(1,1,1), vec c=(0,1,-1)a...

Given that `veca=(1,1,1), vec c=(0,1,-1)and veca. vecb=3`. If `veca xx vecb=vec c`, then `vecb=`

A

`((1)/(2),-(1)/(2),(1)/(2))`

B

`((2)/(3),(2)/(3),(4)/(3))`

C

`((5)/(3),(2)/(3),(2)/(3))`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have,
`veca xx vecb xx vec c`
`rArr" "veca xx(veca xx vecb)=veca xx vec c`
`rArr" "(veca. vecb)veca-(veca.veca)vecb=veca xx vec c`
`rArr" "3veca-3vecb=-2hati+hatj+hatk`
`rArr" "3hati+3hatj+3hatk-3hatb=-2hati+hatj+hatk`
`rArr" "vecb=(1)/(3)(5hati+2hatj+2hatk)`
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