> [!summary] The unit vector of a vector $\vec{v}$ preserves the direction at length 1 > **Key Equations:** $\vec{u}=\frac{\vec{v}}{||\vec{v}||}$ >[!info]+ Read Time **⏱ 1 min** # Definition If $\vec{v}$ is a nonzero vector, then $\vec{u}=\frac{\vec{v}}{||\vec{v}||}$ is the unit vector of $\vec{v}$, which is found of the vector $\vec{v}$ over the [[Vector Length|magnitude]] of $\vec{v}$. $\vec{u}$ is in the direction of $\vec{v}$ with length 1. > [!note]- Proof of Unit Vector equaling 1 > $ ||\vec{u}|| = \left| \left| \frac{1}{||\vec{v}||} \vec{v} \right| \right| = \frac{||\vec{v}||}{||\vec{v}||}=1 > $ # Resources <iframe width="560" height="315" src="https://www.youtube.com/embed/baWg4xA_PjA?si=IsIgQa3eL75HDKYs" title="YouTube video player" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>