The vector `vec(a) ` lies in the plane of vectors `vec(b) and vec(c)`. Which one of the following is correct ?

Options

A. `vec(a).(vec(b)xxvec(c))=0`
B. `vec(a).(vec(b)xxvec(c))=1`
C. `vec(a).(vec(b)xxvec(c))=-1`
D. `vec(a).(vec(b)xxvec(c))=3`

Answer

A

Explanation

Let the vector `vec(a)` lies in the plane of vectors `vec(b) and vec(c)`.
`rArr vec(a), vec(b) and vec(c)` are coplanar.
`:.vec(a).(vec(a)xxvec(c))=0`