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Unit vector in the direction of $$$\left\langle 2 t, 2\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle 2 t, 2\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = 2 \sqrt{t^{2} + 1}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{t}{\sqrt{t^{2} + 1}}, \frac{1}{\sqrt{t^{2} + 1}}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle 2 t, 2\right\rangle$$$A is $$$\left\langle \frac{t}{\sqrt{t^{2} + 1}}, \frac{1}{\sqrt{t^{2} + 1}}\right\rangle = \left\langle \frac{t}{\left(t^{2} + 1\right)^{0.5}}, \left(t^{2} + 1\right)^{-0.5}\right\rangle.$$$A