If `4 vec a+5 vec b+9 vec c=0,` then `( vec axx vec b)xx[( vec bxx vec c)xx( vec cxx vec a)]` is equal to a. vector perpendicular to the plane of`a ,b ,c` b. a scalar quantity c. ` vec0` d. none of these

Options

A. a vector perpendicular to the plane of `veca, vecb and vecc`
B. a scalar quantity
C. `vec0`
D. none of these

Answer

c

Explanation

`4 veca + 5 vecb + 9 vecc =0`
`Rightarrow "vcectors" veca,vecb and vecc` are coplanar.
`Rightarrow vecb xx vecc and vecc xx veca` are collinear.
`Rightarrow (vecb xx vecc) xx (vecc xx veca) = vec0`