Three vector `vec(A)`,`vec(B)`, `vec(C )` satisfy the relation `vec(A)*vec(B)=0`and `vec(A).vec(C )=0`. The vector `vec(A)` is parallel to

Options

A. `vec(b)`
B. `vec(c)`
C. `vec(b).vec(c )`
D. `vec(b)xxvec(c )`

Answer

D

Explanation

`vec(a).vec(b)=0` i.e., `vec(a)` and `vec(b)` will be perpendicular to each other
`vec(a).vec(c )=0 i.e., vec(a)` and `vec(c )` will be perpendicular to each other.
`vec(b)xxvec(c )` will be a vector perpendicular to both `vec(b)` and `vec(c )`
So `vec(a)` is parallel to `vec(b)xxvec(c )`