## Elementary Linear Algebra 7th Edition

(a) $$u =(4,4,3).$$ (b)$$u =(-4,-4,-3).$$ (c) $$u =(-16,-16,-12).$$
Let $v=(8,8,6)$, then we have (a) Since $u$ in the direction of $v$ then $u=cv$ ($c>0$). Since the length of $u$ is one-half of $v$, then $c=\frac{1}{2}$. Hence, $$u=\frac{1}{2}(8,8,6)=(4,4,3).$$ (b) Since $u$ in the direction opposite that of $v$ then $u=-cv$ ($c>0$). Since the length of $u$ is one-fourth of $v$, then $c=\frac{1}{4}$. Hence, $$u=-\frac{1}{4}(8,8,6)=(-4,-4,-3).$$ (c) Since $u$ in the direction opposite that of $v$ then $u=-cv$ ($c>0$). Since the length of $u$ is twice of $v$, then $c=2$. Hence, $$u=-2(8,8,6)=(-16,-16,-12).$$