How to square a velocity vector?

Question

I've just looked at Bernoulli's equation $\frac 12 \mathbf V^2- \Phi+\frac{p}{\rho}=\rm constant$. Since $\mathbf V$ is a velocity vector how is it squared? Is each component squared separately?

Answer 1

$\mathbf V^2$ simply means $\mathbf V \cdot \mathbf V $, where $\cdot $ is the Dot product. It implies the squared norm $\|\mathbf V\|^2$.