Step by Step Solver to Find the Unit Vector in the Opposite Direction to a Given Vector

Step by Step Solver to Find the Unit Vector
in the Opposite Direction to a Given Vector

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












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




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