Are two vectors in the same direction if their dot product is greater than zero/positive? I know they are orthogonal if their dot product is 0 so they can not be in the same direction. I also read if a vector u is scalar multiple of v, they are in the same direction? I can not find a definitive answer.
[Math] Two vectors are in the same direction if
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Best Answer
Two vectors $\mathbf v$ and $\mathbf w$ are in the same direction if and only if $$\frac{\mathbf{v}}{v}\cdot\frac{\mathbf{w}}{w}=1$$
One of the many ways your can rephrase this is $\mathbf{\hat v}=\mathbf{\hat w}$. You are right that they are scalar multiples.