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spndsh
when do you use the dot product?
the most simple answer I can give you to that very general question when you want to determine how parallel two lines are, or the angle between them
ok, how do you use dot product to find a vector projection?
Given two vector \(\vec a\) and \(\vec b\) the projection of \(\vec b\) onto \(\vec a\) is given by\[\text{proj}_{\vec a}\vec b={\vec a\cdot\vec b\over\|\vec a\|^2}\vec a\]
where \[\|\vec a\|\] is the magnitude of \(\vec a\)