# Find the Unit Vector in the Opposite Direction to a Given Vector

An interactive step by step calculator to find the unit vector in the opposite direction of a given vector is presented. The solver may also be used to generate as many examples as needed along with their solutions with detailed explanations. 1) The magnitude $||\vec{v}||$ of a vector $ \vec{v} $ given by its components as $\vec{v} = \langle a, b \rangle $ is given by $||\vec{v}||=\sqrt{a^2+b^2}$2) The unit vector $\vec{u}$ in the opposite direction as vector $\vec{v}$ is given by : $\vec{u} = -\dfrac{1}{||\vec{v}||} \vec{v}.$ Solve each step below then click on "Show me" to check your answer. Check the sketch of the given vector and the unit vector opposite to it at the bottom of the page. Step by step solution |