## anonymous 4 years ago when do you use the dot product?

1. TuringTest

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

2. anonymous

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

3. TuringTest

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

4. TuringTest

where $\|\vec a\|$ is the magnitude of $$\vec a$$

5. anonymous

oh, thanks so much!

6. TuringTest

welcome!