Find the Unit Vector in the Same Direction as a Given Vector

An interactive Step by step calculator and solver that generates examples to calculate the unit vector in the same direction as a given vector is presented. As many examples as needed may be generated along 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 same 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 at the bottom of the page.

Step by step solution











Below are shown the given vector (green) and the unit vector (red) in the same direction.




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