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`(given) `rArr vec(A)_|_vec(B)`
`vec(A).vec(C )=0` (given) `rArr vec(A)_|_vec(C )`
`vec(A)` is perpendicular to both `vec(B)` and `vec(C )`.
We know from the defination of cross product that `vec(B)xxvec(C )` is perpendicular to both `vec(B)` and `vec(C )`.
So `vec(A)` is parallel to `vec(B)xxvec(C )`.