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Unit vector in the direction of $$$\left\langle \frac{1}{2} - \frac{\sqrt{5}}{2}, 1\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle \frac{1}{2} - \frac{\sqrt{5}}{2}, 1\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{10 - 2 \sqrt{5}}}{2}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{- \sqrt{10} + \sqrt{2}}{2 \sqrt{5 - \sqrt{5}}}, \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}}}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle \frac{1}{2} - \frac{\sqrt{5}}{2}, 1\right\rangle$$$A is $$$\left\langle \frac{- \sqrt{10} + \sqrt{2}}{2 \sqrt{5 - \sqrt{5}}}, \frac{\sqrt{2}}{\sqrt{5 - \sqrt{5}}}\right\rangle\approx \left\langle -0.525731112119134, 0.85065080835204\right\rangle.$$$A