If `vec(A)xxvec(B)= vec(C )+vec(D)`, then select the correct alternative.

Options

A. `vec(B)` is parallel to `vec(C )+vec(D)`
B. `vec(A)` is perpendicualr to `vec(C )`.
C. Components of `vec(C )` along `vec(A)`= component of `vec(D)` along `vec(A)`
D. Component of `vec(C )` along `vec(A)`= -component of `vec(D)` along `vec(A)`

Answer

D

Explanation

According to defination of cross- product `vec(C )+vec(D)` is perpendicualr to both `vec(A)` and `vec(B)`.
i.e., `vec(A).(vec(C )+vec(D))=0`
or `vec(A).vec(C )+vec(A).vec(D)=0`
or A(component of `vec(C )` along `vec(A)`)+A(component of `vec(D)` along `vec(A))=0`
or component of `vec(C )` along `vec(A)`= -component of `vec(D)` along `vec(A)`