Vectors $a_{1}$, $a_{2}$, ..., aₙ are linearly dependent if there exist scalars $c_{1}$, $c_{2}$, ..., cₙ (not all zero) such that $c_{1}$$a_{1}$ + $c_{2}$$a_{2}$ + ... + cₙaₙ = 0. Otherwise they are linearly independent. In 3D: (1) Two vectors are linearly dependent iff they are collinear. (2) Three vectors are linearly dependent iff they are coplanar (scalar triple product = 0). (3) Any set of four or more vectors in 3D is always linearly dependent. Three linearly independent vectors form a basis for 3D space — any vector can be expressed as a unique linear combination of them.