# Unit vector in the direction of $\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle$

The calculator will find the unit vector in the direction of the vector $\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle$, with steps shown.
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Find the unit vector in the direction of $\mathbf{\vec{u}} = \left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle$.

### Solution

The magnitude of the vector is $\mathbf{\left\lvert\vec{u}\right\rvert} = 2$ (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 $\mathbf{\vec{e}} = \left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle$ (for steps, see vector scalar multiplication calculator).

The unit vector in the direction of $\left\langle 2 \cos{\left(t \right)}, - 2 \sin{\left(t \right)}, 0\right\rangle$A is $\left\langle \cos{\left(t \right)}, - \sin{\left(t \right)}, 0\right\rangle$A.