Prove that two vectors are perpendicular without having coordinates of vectors

Question

Homework: Two vectors that are $\neq\vec{0}$ have a dot product equal to 0. Prove that they are perpendicular.

Answer 1

Hint: Since the two vectors aren't null vectors, we have: $$\vec v\bullet\vec u=\|\vec v\|\|\vec u\|\cos\theta=0\iff \cos\theta=0$$ where $\theta$ is the angle between the two vectors.