1. Home
  2. Calculators
  3. Calculators: Linear Algebra
  4. Linear Algebra Calculator

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

The calculator will find the unit vector in the direction of the vector $$$\left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle$$$, with steps shown.
$$$\langle$$$ $$$\rangle$$$
Comma-separated.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

Your Input

Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle - \frac{\cos{\left(t \right)}}{2}, 0, - \frac{\sin{\left(t \right)}}{2}\right\rangle$$$.

Solution

The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{1}{2}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle - \cos{\left(t \right)}, 0, - \sin{\left(t \right)}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).

Answer

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