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For any two vectors A and B, if vec(A).v...

For any two vectors A and B, if `vec(A).vec(B) = |vec(A) xx vec(B)|`, the magnitude of `vec(C ) = vec(A) + vec(B)` is equal to :

A

`sqrt(A^(2) + B^(2))`

B

`A+ B`

C

`sqrt(A^(2) + B^(2) + (AB)/(sqrt2))`

D

`sqrt(A^(2) + B^(2) + sqrt2 xx AB)`

Text Solution

Verified by Experts

The correct Answer is:
D
`vec(A).vec(B)= |vec(A) xx vec(B)|`
`rArr AB cos theta = AB sin theta rArr tan theta=1 rArr theta= 45^(@)`
`|vec(C)|= sqrt(A^(2) + B^(2) + 2AB cos 45^(@))= sqrt(A^(2) + B^(2) + 2AB xx (1)/(sqrt2))`
`|vec(C)| = sqrt(A^(2) + B^(2) + sqrt2AB)`
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