Answer
(a) $4$
(b) $4j$
(c) $4j$, $2i$
Work Step by Step
(a) Given $\vec u=2i+4j=\langle 2, 4 \rangle$ and $\vec v=0i+10j=\langle 0, 10 \rangle$，we have
$comp_v\vec u=\frac{\vec u\cdot\vec v}{|\vec v|}=\frac{2\times0+4\times(10)}{\sqrt {0^2+(10)^2}}=\frac{40}{10}=4$
(b) $proj_v\vec u=(\frac{\vec u\cdot\vec v}{|\vec v|^2})\vec v=-\frac{40}{100}\langle 0, 10 \rangle=\langle 0, 4 \rangle=4j$
(c) Clearly $\vec u_1=proj_v\vec u=4j$, and $\vec u_2=\vec u-\vec u_1=\vec u-proj_v\vec u=(2-0)i+(4-4)j=2i$
