Answer
(a) $\| u \| = 2$
(b) $\| v \| =\sqrt{\langle v, v\rangle}= \sqrt{10}$
(c) $\langle u, v \rangle = 2$
(d) $d(u,v) =\sqrt{10}.$
Work Step by Step
Let $u=(1,-1,0,1,1), \quad v=(0,1,-2,2,1)$, then we have
(a) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2+u_3^2+u_4^2+u_5^2}=2$
(b) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2+v_4^2+v_5^2}=\sqrt{10}$
(c) $\langle u, v \rangle =u_1v_1+u_2v_2+u_3v_3+u_4v_4+u_5v_5= 2$
(d) $d(u,v)=\| u-v \|=\| (1,-2,2,-1,0) \|=\sqrt{10}.$
