Two vectors and the angle between them.

[exitwound]

Homework Statement

An electron follows a helical path in a uniform magnetic field given by B = (20i - 50j - 30k ) mT. At time t = 0, the electron's velocity is given by v = (17i - 32j + 53k ) m/s.

(a) What is the angle ϕ between v and B?

Now, I have the answer from help from someone else. However, I don't understand the reasoning. The solution was to take: $$cos \phi = \frac{\vec v \cdot \vec B}{|\vec v| |\vec B|}$$ solving for ϕ.

Can anyone explain it to me?

 

[CompuChip]

It's simply the formula for the dot product:

for any vectors a and b,
$$\vec a \cdot \vec b = |\vec a| |\vec b| \cos\phi,$$
where $\phi$ is the angle between the two vectors.

 

[exitwound]

OH! That NEVER occurred to me.