A set of vectors u₁, u₂,…, u_r is linearly independent if x₁u₁ + x₂u₂ + … + x_ru_r = 0 implies x₁ = 0, x₂ = 0,…, x_r = 0. Otherwise, the set is linearly dependent. A set of two vectors is linearly independent if and only if the two are not parallel or, in other words, if and only if neither is a scalar multiple of the other. In 3‐dimensional space, any set of four or more vectors must be linearly dependent, and a set of three vectors is linearly independent if and only if the three are not coplanar. See basis.