# Unit Vector and Components of a Vector

### Unit Vector

A

unit vector is a vector with a magnitude of one unit.

Any vector has an associated unit vector in the same direction but having a magnitude of one. Any vector can be
expressed as a scalar multiple
of its unit vector.

Related Topics:

Vectors

Unit Vectors in Physics

Next set of math lessons in this series

Finding the Unit Vector given a vector (divide the vector by its magnitude).

Finding the vector

**u** given the initial point and the terminal point, then finding the length of the vector and finally finding the unit vector.

Unit vectors have a magnitude of one, and the specific unit vectors

**i** and

**j**
represent the positive horizontal and vertical unit vectors in a two dimensional plane. We can write any two
dimensional vector in terms of these two unit vectors, and that notation is often seen in Calculus.

How to express a vector algebraically in terms of the unit vectors

**i** and

**j**.

This video explains how to determine a unit vector given a vector. It also explains how to determine the component form of a vector in standard position that intersects the unit circle.

Expressing a vector as the scaled sum of unit vectors.

Unit Vector Notation (part 2).

Showing that adding the

**i** and

**j** components of two vectors is equivalent to adding the vectors visually using the head-to-tail method.

Next set of videos in this series