Chapter 5 - Inner Product Spaces - Review Exercises - Page 284: 9

$$\| v \| = \sqrt{38}.$$ $$\frac{1}{\| v \|}v=\frac{1}{38}(5,3,-2)$$

Let $ v=(5,3,-2)$, then we have $$\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2 }=\sqrt{38}.$$ The unit vector in direction of $v$ is given by $$\frac{1}{\| v \|}v=\frac{1}{38}(5,3,-2)$$