1. ## vector question

given two vectors, $\displaystyle \vec{u}$ and $\displaystyle \vec{v}$ such that $\displaystyle \vec{u} \cdot \vec{v} = |\vec{u}| |\vec{v}|$ explain what you know about these two vectors.

2. What ideas have you had so far?

3. the only thing i can think of is that one of them has a length of 0.

4. Yes, if either of the vectors, or both, are the zero vector, the equation will hold. What if neither are nonzero? Can you still satisfy the equation?

5. How do you find the angle between two vectors usually?

Maybe this will hint you at the answer

6. does this mean there is no angle between the two vectors? (0 deg)

7. Right. That's the only situation where the angle between the two vectors has a cosine of one.

8. And, of course, having an angle of "0" between them means the vector point in the same direction- one is a multiple of the other. (We should also point out that $\displaystyle cos(180)= 0$. Two angles that point in opposite directions have dot product 0. Of course, one is still a multiple of the other, just with negative multiplier.)

I think you meant to say that $\displaystyle \cos(180^{\circ})=-1.$ If two vectors are pointed in the opposite direction, then the cosine of their angle is negative one. Two vectors that are orthogonal have a zero dot product.