# Unit vector in the direction of $$$\left\langle 2 e^{2 t}, 0\right\rangle$$$

### Your Input

**Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle 2 e^{2 t}, 0\right\rangle$$$.**

### Solution

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

### Answer

**The unit vector in the direction of $$$\left\langle 2 e^{2 t}, 0\right\rangle$$$A is $$$\left\langle 1, 0\right\rangle$$$A.**