Given the vector vec$(v)=3$vec$(i)+4$vec$(j)$ and force vector vec$(F)=15$vec$(i)+20$vec$(j),$ find:

$($a$)$ The component of vec$(F)$ parallel to vec$(v).$

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vec$(F{)}_{\text{p}\text{a}\text{r}\text{a}\text{l}\text{l}\text{e}\text{l}}=i,$vec$(i)$

$($b$)$ The component of vec$(F)$ perpendicular to vec$(v).$

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vec$(F{)}_{\text{p}\text{e}\text{r}\text{p}}=vec(i)$

$($c$)$ The work, $W,$ done by force vec$(F)$ through displacement vec$(v).$

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$W=$

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