If `vecA xx vecB = vecC+ vecD`, them select the correct alternative:

Options

A. `vecB` is parallel to `vecC + vecD.`
B. `vecA` is perpendicular to `vecC.`
C. Component of `vecC` along `vecA` = component of `vecD` along `vecA`
D. Component of `vecC` along `vecA =` - component of `vecD` along `vecA`

Answer

D

Explanation

According to definition of cross-product `vec(C)+vec(D)` is perpendicular to both `vec(A)andvec(B)`
i.e., `vec(A).(vec(C)+vec(D))=0orvec(A). vec(C)+vec(A).vec(D)=0`
or A (component of `vec(C)` along `vec(A)`) + A(component of `vce(D)` along `vec(A)`)=0
or component of `vec(C)` along `vec(A)` =- component of `vec(D)` along `vec(A)`