Given vector $v=3i+4j$ and force vector $\vec F=0.2\vec i-0.5\vec j$, find the component of $\vec F$ parallel to $\vec v$.

Question

The solution is $-0.168\vec i-0.224\vec j$. I have the formula $F_{||}=(F•u)u$ and $\vec F=\vec F_{||}+\vec F_{\perp}$, but I am not sure how to relate these to v.

Answer 1

Dear Emily projection of $F$ on $v~$: $F_{v} =\frac{F.v}{v.v}\frac{v}{|v|}=-\frac{1.4}{125}v$