What is Scalar product?

The scalar product of two vectors $\vec u$ and $\vec v$ is the number

where $\norm{\vec u}$ denotes the length (norm) of $\vec u$.

The scalar product of $\vec u$ and $\vec v$ is

where $\norm{\vec u}$ is the length of $\vec u$. If both vectors are nonzero, $\vec u \cdot \vec v = \norm{\vec u}\,\norm{\vec v}\cos\theta$ where $\theta$ is the angle between them; and in an orthonormal coordinate system,

Two vectors are orthogonal if their scalar product is $0$.