Unit vector

Unit vector (or often normalized vector) is a vector of length 1 (one)

Unit vector is denoted by \(\hat{Q}\) (pronounced "q-hat")

The unit vector \(\hat{Q}\) of a non-zero vector \(\vec{ Q }\) is the vector in the direction of \(\vec{ Q }\) and with the length equal to 1 (one):

\( \hat{Q}=\dfrac{\vec{ Q }}{\lVert \vec{ Q } \rVert} \)

For a \(two\)-dimensional vector \(\vec{ Q }\), used in current example:

\( \hat{Q}=\dfrac{\vec{ Q }}{\lVert \vec{ Q } \rVert}=\Biggl \langle \dfrac{Q_x}{\sqrt{Q_x^2 + Q_y^2}}, \dfrac{Q_y}{\sqrt{Q_x^2 + Q_y^2}} \Biggr \rangle \)