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सिद्ध कीजिए कि |vecA xx vecB|^(2) + |vec...

सिद्ध कीजिए कि `|vecA xx vecB|^(2) + |vecA * vecB|^(2) = (AB)^(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)andvce(B)`
`:.|vec(A)xxvec(B)|=ABsinthetaand|vec(A).vec(B)|=ABc ostheta`
`:.|vec(A)xxvec(B)|^(2)+|vec(A).vec(B)|^(2)=(ABsintheta)^(2)+(ABcostheta)^(2)`
`=A^(2)B^(2)sin^(2)cos^(2)theta=A^(2)B^(2)`
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