In 3D space, vectors can be tested for linear dependence: two vectors are dependent (collinear) iff one is a scalar multiple of the other (a x b = 0). Three vectors are dependent (coplanar) iff [a b c] = 0. Any four or more vectors in 3D are always linearly dependent. Three linearly independent vectors form a basis — any vector can be uniquely expressed as their linear combination. To find coefficients: if r = xa + yb + zc, then x = [r b c]/[a b c]. Four points are coplanar iff [AB AC AD] = 0. Collinear points satisfy AB = lambda · AC for some scalar lambda. These tests are among the most commonly asked concepts in JEE vector algebra.