Question

when do you use the dot product?

Answer 1

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

Answer 2

ok, how do you use dot product to find a vector projection?

Answer 3

Given two vector \(\vec a\) and \(\vec b\) the projection of \(\vec b\) onto \(\vec a\) is given by\[\text{proj}_{\vec a}\vec b={\vec a\cdot\vec b\over\|\vec a\|^2}\vec a\]

Answer 4

where \[\|\vec a\|\] is the magnitude of \(\vec a\)

Answer 5

oh, thanks so much!

Answer 6

welcome!