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If vec(A)xxvec(B)=vec(C ), then which of...

If `vec(A)xxvec(B)=vec(C )`, then which of the following statements is wrong?

A

`vecCbotvecA`

B

`vecCbotvecB`

C

`vecCbot(vecA+vecB)`

D

`vecCbot(vecAxxvecB)`

Text Solution

Verified by Experts

The correct Answer is:
D
From the property of vector product, we notice that `vecC` must be perpendicular to the plane formed by vector `vecA` and `vecB`. Thus `vecC` is perpendicular to both `vecA` and `vecB` and `(vecA+vecB)` vector also must lie in the plane formed by vector `vecA` and `vecB`.Thus `vecC` must be perpendicular to `(vecA+vecB)` but the cross product `(vecAxxvecB)` gives a vector `vecC` which cannot be perpendicular to itself. Thus the last statement is wrong.
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