Answer
(a) $\langle u, v\rangle =-2$
(b) $d(u,v)=\sqrt{\frac{99}{4}}$.
Work Step by Step
$u=(2,-\frac{1}{2},1), \quad v=(\frac{3}{2},2,-1)$, $\langle u, v \rangle =u_1v_1+2u_2v_2+3u_3v_3 $.
(a) $\langle u, v\rangle =u_1v_1+2u_2v_2+3u_3v_3=3-2-3=-2$
(b) $d(u,v)=\| u-v \|=\| (\frac{1}{2},-\frac{5}{2},2) \|=\sqrt{\frac{1}{4}+\frac{25\times 2}{4}+4\times 3}=\sqrt{\frac{99}{4}}$.