Answer
(a) $\| u \| = \sqrt{6}$
(b) $\| v \| = =\sqrt{3}$
(c) $\langle u, v \rangle = -1$
(d) $d(u,v)= \sqrt{11}.$
Work Step by Step
Let $u=(1,-2,0,1), \quad v=(1,1,-1,0)$, then we have
(a) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2+u_3^2}=\sqrt{6}$
(b) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2}=\sqrt{3}$
(c) $\langle u, v \rangle =u_1v_1+u_2v_2+u_3v_3= -1$
(d) $d(u,v)=\| u-v \|=\| (0,-3,1,1) \|=\sqrt{11}.$
