Answer
(a) $\langle u, v \rangle = -12$
(b) $\| u \| = \sqrt{72}$
(c) $\| v \| = \sqrt{3}$
(d) $d(u,v)= \sqrt{99}$
Work Step by Step
$u=(0,-6), \quad v=(-1,1)$
(a) $\langle u, v \rangle =u_1v_1+2u_1v_2=0-12=-12$
(b) $\| u \| =\sqrt{\langle u, u\rangle}=\sqrt{u_1^2+2u_2^2}=\sqrt{0+72}=\sqrt{72}$
(c) $\| v \| =\sqrt{\langle v, v\rangle}=\sqrt{v_1^2+2v_2^2}=\sqrt{3}$
(d) $d(u,v)=\| u-v \|=\| (1,-7 \|=\sqrt{1 +2(49)}=\sqrt{99}$
