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Four vectors veca, vecb, vecc and vecx s...

Four vectors `veca, vecb, vecc` and `vecx` satisfy the relation `(veca.vecx)vecb=vecc+vecx` where `vecb.veca ne 1`. The value of `vecx` in terms of `veca, vecb` and `vecc` is equal to

A

`((veca.vecc)vecb-vecc(veca.vecb-1))/((veca.vecb-1))`

B

`vecc/(veca.vecb-1)`

C

`(2(veca.vecc)vecb+vecc)/(veca.vecb-1)`

D

`(2(veca.vecc)vecc+vecc)/((veca.vecb)-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
`(veca.vecx)vecb=vecc+vecx`…………..(i)
taking dot with `veca`
`(veca.vecx)(vecb.veca)=(vecc.veca)+(veca.vecx)`
`therefore (veca.vecx)(vecb.veca-1)=(vecc.veca)`
`therefore (veca.vecx)=(vecc.veca)/(vecb.veca-1)`
`rArr vecx=(vecc.veca)/(vecb.veca-1)vecb-vecc`
`=((veca.vecc)vecb-vecc(veca.vecb-1))/(veca.vecb-1)`
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