> [!NOTE] Lemma > Let $n\geq 1.$ Let $\underline{v}\in \mathbb{R}^{n}\setminus\{ \underline{0} \}$ be a [[Real n-Space|n-tuple of reals]] that is not [[Real Zero Vector|zero]]. Let $||\underline{v}||$ denote its [[Euclidean Norm|length]]. Then the [[Scalar Multiplication in Real n-Space|scalar multiple]] $\underline{\hat{v}}=\frac{1}{||\underline{v}||}\underline{v}$is a vector of length $1$ that is [[Collinearity in Real n-Space|collinear]] with $\underline{\hat{v}}.$ **Proof**: Follows from [[Length of Scaled Real Vector]] by setting $\lambda=\frac{1}{||\underline{v}||}$ which is strictly greater zero by [[Non-negative Definiteness of Length of Real Vector]] since $\underline{v}\neq \underline{0}.$