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Unit vector in the direction of $$$\left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$

The calculator will find the unit vector in the direction of the vector $$$\left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$, with steps shown.
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Your Input

Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$.

Solution

The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{1}{3}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle - \sin{\left(t \right)}, - \cos{\left(t \right)}, 0\right\rangle$$$ (for steps, see vector scalar multiplication calculator).

Answer

The unit vector in the direction of $$$\left\langle - \frac{\sin{\left(t \right)}}{3}, - \frac{\cos{\left(t \right)}}{3}, 0\right\rangle$$$A is $$$\left\langle - \sin{\left(t \right)}, - \cos{\left(t \right)}, 0\right\rangle$$$A.