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Unit vector in the direction of $$$\left\langle 1, 3, 2\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle 1, 3, 2\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \sqrt{14}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{\sqrt{14}}{14}, \frac{3 \sqrt{14}}{14}, \frac{\sqrt{14}}{7}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle 1, 3, 2\right\rangle$$$A is $$$\left\langle \frac{\sqrt{14}}{14}, \frac{3 \sqrt{14}}{14}, \frac{\sqrt{14}}{7}\right\rangle\approx \left\langle 0.267261241912424, 0.801783725737273, 0.534522483824849\right\rangle.$$$A