If `veca xx vecb = vecb xx vecc ne 0 ` where `veca , vecb and vecc` are coplanar vectors, then for some scalar k prove that `veca+vecc = kbvecb`.

Options

A. `veca,vecb and vecv` can be coplanar
B. `veca, vecb and vecc` must be coplanar
C. `veca,vecb and vecc` cannot be coplanar
D. none of these

Answer

c

Explanation

`(veca xx vecb) xx (vecb xx vecc) = vecb`
` or [veca vecb vecc] vecb = vecb`
` or [veca vecb vecc] =1 `
therefore, `veca , vecb and vecc` cannot be coplanar.