If the vectors a , b and c are coplanar, then | array ccc a & b & c a a & a b & a c b a & b b & b c array | is equal to

Step-by-step solution

Since, a , b and c are coplanar, there must exists three scalars x, y and z are not all zero such that x a +y b +z c =0 Multiplying both sides of Eq. (i) by a and b respectively, we get array l x a a +y a b +z a c =0 x b a +y b b +z b c =0 array Eliminating x, y and z from Eqs. (i), (ii) and (iii), we get | array ccc a & b & c a a & a b & a c b a & b b & b c array |=0