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Unit vector in the direction of $$$\left\langle \frac{211}{69}, - \frac{84}{23}, - \frac{17}{69}, \frac{272}{69}, 1\right\rangle$$$
Your Input
Find the unit vector in the direction of $$$\mathbf{\vec{u}} = \left\langle \frac{211}{69}, - \frac{84}{23}, - \frac{17}{69}, \frac{272}{69}, 1\right\rangle$$$.
Solution
The magnitude of the vector is $$$\mathbf{\left\lvert\vec{u}\right\rvert} = \frac{\sqrt{187059}}{69}$$$ (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 $$$\mathbf{\vec{e}} = \left\langle \frac{211 \sqrt{187059}}{187059}, - \frac{84 \sqrt{187059}}{62353}, - \frac{17 \sqrt{187059}}{187059}, \frac{272 \sqrt{187059}}{187059}, \frac{\sqrt{187059}}{2711}\right\rangle$$$ (for steps, see vector scalar multiplication calculator).
Answer
The unit vector in the direction of $$$\left\langle \frac{211}{69}, - \frac{84}{23}, - \frac{17}{69}, \frac{272}{69}, 1\right\rangle$$$A is $$$\left\langle \frac{211 \sqrt{187059}}{187059}, - \frac{84 \sqrt{187059}}{62353}, - \frac{17 \sqrt{187059}}{187059}, \frac{272 \sqrt{187059}}{187059}, \frac{\sqrt{187059}}{2711}\right\rangle\approx \left\langle 0.487857685579326, -0.582654676616067, -0.039306069454258, 0.628897111268136, 0.159536399549637\right\rangle.$$$A