An online calculator to calculate the unit vector in the direction of a vector given by its components.

Unit Vector of a 2-D Vector

Let \( \vec v \) be a vector given in component form by
\( \vec v = \; \lt v_x , v_y \gt \)
The unit vector \( \vec {v}_u \) of vector \( \vec v \) is given by
\[ \large \color{red} {\vec v_u = \; \lt \dfrac{v_x}{|\vec v|} , \dfrac{v_y}{|\vec v|} \gt} \]
where \( |\vec v| \) is the magnitude of vector \( \vec v \) and is given by
\( |\vec v| = \sqrt {v^2_x + v^2_y} \)

Unit Vector of a 3-D Vector

Let \( \vec v \) be a vector given in component form by
\( \vec v = \; \lt v_x , v_y , v_z \gt \)
The unit vector \( \vec {v}_u \) of vector \( v \) is given by
\[ \large \color{red} { \vec v_u = \; \lt \dfrac{v_x}{|\vec v|} , \dfrac{v_y}{|\vec v|} , \dfrac{v_z}{|\vec v|} \gt } \]
where \( |\vec v| \) is the magnitude of vector \( \vec v \) and is given by
\( |\vec v| = \sqrt {v^2_x + v^2_y + v^2_z } \)

2-D Unit Vector Calculator

3-D Unit Vector Calculator

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