Answer
(a) $\| u \| = \sqrt{5}$
(b) $\| v \| = \sqrt{17}$
(c) $u\cdot v =6$
(d) $d(u,v)=\sqrt{10}.$
Work Step by Step
Let $u=(1,2), \quad v=(4,1)$, then we have
(a) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2}=\sqrt{5}$
(b) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2}=\sqrt{17}$
(c) $u\cdot v =u_1v_1+u_1v_2=6$
(d) $d(u,v)=\| u-v \|=\| (-3,1) \|=\sqrt{10}.$
