Skip Ahead:

Main Vector Page | x-axis Unit Vector | y-axis Unit Vector | 2D Unit Vector | 3D Unit Vector

The Unit Vector

Unit Vector in 1D y-axis

A Unit Vector is a vector with a magnitude (length) of 1.

In the simulation below, you can see a unit vector, of variable angle and direction, however with a constant magnitude of 1, based on the movement of your mouse over the simulation. Regardless of which direction the unit vector is pointing, whether that be the positive or negative y-axis, or any angle it is in, 90 or 270, the magnitude of the unit vector will always be positive 1.

A unit vector can be represented in numerous ways. Here are the three most common ways of portraying them:

\[ \vec{B} = \begin{bmatrix} \hat{i} & \hat{j} & \hat{k} \\ 0 & 1 & 0 \end{bmatrix} \]

or

\[ \vec{B} = 0\hat{i} + 1\hat{j} + 0\hat{k} \]

or

\[ \vec{B} = \langle 0, 1, 0 \rangle \]

A unit vector can be calculated using the folliwng equation:

\[ \hat{u} = \frac{u}{|\text{u}|} \]

û is the normalized vector, u is a non-zero vector, and |u| is the magnitude (length) of the vector u.

In this example, the vector is a non-zero vector〈0, 1, 0〉of magnitude 1. So the equation now becomes:

\[ \hat{u} = \frac{\langle 0, 1, 0 \rangle}{|1|} = 1 \]

Here the û normalized vector is equal to 1. This is the case for all unit vectors.

Go Back to x-axis Unit Vector 2D Unit Vector