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 xx vec C`
D. `vec B cdot vec C`

Answer

C

Explanation

`vec A cdot vec B =AB cos theta =0." for this " theta =90^(@)" or "vec A bot vec B`
`vec A cdot vec C = AC cos theta =0" "therefore theta =90^(@) and vec A bot vec C`
`vec A` is perpendicular to both `vec B and vec C`
The vector `vec B xx vec C` is perpendicular to the plane formed by `vec B and vec C`
`therefore vec A` is parallel to `vec B xx vec C`