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Three vectors veca,vecb,vecc are such th...

Three vectors `veca,vecb,vecc` are such that `veca xx vecb=4(veca xx vecc)` and `|veca|=|vecb|=` and `|vecc|=1/4`. If the angle between `vecb` and `vecc` is `pi/3` then `vecb` is

A

`veca + 4vecc`

B

`veca-4vecc`

C

`4vecc-veca`

D

`2vecc-veca`

Text Solution

Verified by Experts

The correct Answer is:
A, C
`veca xx vecb = 4(veca xx vecc)`
`veca xx (vecb-4vecc)=vec0`
`rArr veca = t(vecb-4vecc)`, where t is scalar.
`therefore |veca|^(2)=t^(2){|b^(2)|+16|c|^(2)-8(vecb.vecc)}`
`therefore 1=t^(2){1+16.1/16-8.1.1/4.1/2}`
`therefore 1=t^(2)[1]`
`therefore t=+-1`
`t=+-1`
`therefore veca=vecb-4vecc` or `veca=vecb+4vecc`
`rArr vecb=veca+4vec`or `vecb=4vecc-veca`
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