## Elementary Linear Algebra 7th Edition

(a) $\|u\|=\frac{3\sqrt{21}}{4 }, \quad \|v\|=\frac{\sqrt{5}}{4}$. (b) Unit vector in direction of $v$ is $\frac{v}{\|v\|}=\frac{4\sqrt{5}}{5}\left(0, \frac{1}{4}, -\frac{1}{2}\right)$. (c) Unit vector in direction opposite to $u$ is $-\frac{u}{\|u\|}=-\frac{4\sqrt{21}}{21}\left(-1, \frac{1}{2}, \frac{1}{4}\right)$. (d) ${u} \cdot {v} =0$. (e)${u} \cdot {u}=\frac{21}{16}$. (f) ${v} \cdot {v}=\frac{5}{16}$.
(a) $\|u\|=\frac{3\sqrt{21}}{4 }, \quad \|v\|=\frac{\sqrt{5}}{4}$. (b) Unit vector in direction of $v$ is $\frac{v}{\|v\|}=\frac{4\sqrt{5}}{5}\left(0, \frac{1}{4}, -\frac{1}{2}\right)$. (c) Unit vector in direction opposite to $u$ is $-\frac{u}{\|u\|}=-\frac{4\sqrt{21}}{21}\left(-1, \frac{1}{2}, \frac{1}{4}\right)$. (d) ${u} \cdot {v} =0$. (e)${u} \cdot {u}=\frac{21}{16}$. (f) ${v} \cdot {v}=\frac{5}{16}$.