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|vec(A)xxvec(B)|^(2)+|vec(A).vec(B)|^(2)...

`|vec(A)xxvec(B)|^(2)+|vec(A).vec(B)|^(2)=`

A

Zero

B

`A^(2)B^(2)`

C

`AB`

D

`sqrt(AB)`

Text Solution

Verified by Experts

The correct Answer is:
B
Let `theta` be angle between Vectors `vec(A)` and `vec(B)`
`:. |vec(A)xxvec(B)|=AB sin theta`
and `|vec(A).vec(B)|= AB cos theta`
`|vec(A)xxvec(B)|^(2)= |vec(A).vec(B)|^(2)=(AB sin theta)^(2)+(AB cos theta)^(2)`
`=A^(2)B^(2)sin^(2)theta+A^(2)B^(2)cos^(2)theta= A^(2)B^(2)`
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