Collinearity of points A, B, C: Points are collinear iff AB x AC = 0, or equivalently AB = k·AC for some scalar k. Collinearity of vectors: a and b are collinear iff a x b = 0, or $a_{1}$/$b_{1}$ = $a_{2}$/$b_{2}$ = $a_{3}$/$b_{3}$. Coplanarity of vectors: a, b, c are coplanar iff [a b c] = a.(b x c) = 0. Coplanarity of four points A, B, C, D: Coplanar iff [AB AC AD] = 0. JEE frequently tests these conditions — always verify using the determinant form.