1.

सिद्ध कीजिए कि `|vecA xx vecB|^(2) + |vecA * vecB|^(2) = (AB)^(2).`A. zeroB. `A^(2)B^(2)`C. ABD. `sqrt(AB)`

Answer» Correct Answer - 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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