Unit Vector Calculator

The calculator will find the unit vector in the direction of the given vector, with steps shown.

$$$\langle$$$ $$$\rangle$$$
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Your Input

Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle 3, 4\right\rangle$$$.

Solution

The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = 5$$$ (for steps, see magnitude calculator).

The unit vector is obtained by dividing each coordinate of the given vector by the magnitude.

Thus, the unit vector is $$$\mathbf{\vec{e}} = \left\langle \frac{3}{5}, \frac{4}{5}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).

Answer

The unit vector in the direction of $$$\left\langle 3, 4\right\rangle$$$A is $$$\left\langle \frac{3}{5}, \frac{4}{5}\right\rangle = \left\langle 0.6, 0.8\right\rangle$$$A.