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If ` vec a` is parallel to ` vec bxx vec c` , then `( vec axx vec b)`.`( vec axx vec c)` is equal to a. `| vec a|^2( vec b . vec c)` b. `| vec b|^2( vec a . vec c)` c. `| vec c|^2( vec a . vec b)` d. none of these

A

`|veca|^(2)(vecb.vecc)`

B

`|vecb|^(2)(veca .vecc)`

C

`|vecc|^(2)(veca.vecb)`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
a
` (veca xx vecb) . (veca xx vecc) = (veca xx vecb) . Vecu, " where " vecu = vecaxx vecc`
` Rightarrow veca. (vecb xx vecu) = veca. [vecb xx (veca xx vecc)]`
`veca . [ (vecb.vecc) veca - (veca. Vecb)vec]`
`=veca . (vecb.vecc) veca ( veca. vecb =0)`
` |veca|^(2) (vecb.vecc)`
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