Unit Vector Calculator
Easily calculate and visualize unit vectors in 2D and 3D. Understand vector normalization and direction with our interactive tool.
Unlock vector directions with ease.
Vector Input
Choose the dimension of your vector.
Enter comma-separated values.
Calculation Results
Calculation Steps:
Unit Vector:
Magnitude:
Vector Visualization
Understanding Unit Vectors
A unit vector, also known as a direction vector, is a vector with a magnitude (or length) of 1. It essentially represents the direction of a vector in space. The process of calculating a unit vector from any given vector is called normalization.
To obtain the unit vector $$ \hat{u} $$ of a given vector $$ \vec{v} $$, you divide each component of $$||\vec{v}||$$ by its magnitude $$||\vec{v}||$$.
Formula: $$ \hat{u} = \frac{\vec{v}}{\|\vec{v}\|} $$
Key Concepts:
- Normalization: The process of scaling a vector to have a magnitude of one.
- Direction Indicator: Unit vectors are primarily used to indicate direction, irrespective of magnitude.
- Applications: Widely used in physics (representing forces and fields), computer graphics (calculating surface normals and lighting directions), and vector analysis for directional computations.
Further reading: Wikipedia - Unit Vectors.