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

Options

A. `vec(C )_|_vec(A)`
B. `vec(C )_|_vec(B)`
C. `vec(C )_|_(vec(A)+vec(B))`
D. `vec(C )_|_(vec(A)xxvec(B))`

Answer

D

Explanation

From the property of vector product, we notice that `vec(C )` must be perpendicular to the plane fromed by vector `vec(A)` and `vec(B)`. Thus `vec(C )` is perpendicular to both `vec(A)` and `vec(B)` and `(vec(A)+vec(B))` vector also, must lie in the plane formed by vector `vec(A)` and `vec(B)`. Thus `vec(C )` must be perpendicular to `(vec(A)+vec(B))` also but the cross product `(vec(A)xxvec(B))` gives a vector `vec(C )` which can not be perpendicular to itself Thus the last staement is Wrong.