Answer
(a) $\| u \| =3$
(b) $\| v \| = =3$
(c) $\langle u, v \rangle = 4$
(d) $d(u,v)= \sqrt{10}.$
Work Step by Step
Let $u=(1,-2,2,0), \quad v=(2,-1,0,2)$, then we have
(a) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+u_2^2+u_3^2}=3$
(b) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+v_2^2+v_3^2}=3$
(c) $\langle u, v \rangle =u_1v_1+u_2v_2+u_3v_3= 4$
(d) $d(u,v)=\| u-v \|=\| (-1,-1,2,-2) \|=\sqrt{10}.$
