Unit vector

Definition

A unit vector is a vector with a magnitude of 1. It is often used to indicate direction without considering the magnitude.

5 Must Know Facts For Your Next Test

1. The magnitude of a unit vector is always 1.
2. To convert any vector into a unit vector, divide the vector by its magnitude.
3. Unit vectors are typically denoted with a hat symbol, such as \( \hat{i} \) or \( \hat{j} \).
4. Unit vectors can be used to express the basis vectors in Cartesian coordinates: \( \hat{i} \), \( \hat{j} \), and \( \hat{k} \).
5. In two dimensions, if a vector has components (a,b), its corresponding unit vector is given by $$\left(\frac{a}{\sqrt{a^2+b^2}},\frac{b}{\sqrt{a^2+b^2}}\right)$$.

Review Questions

• What is the magnitude of a unit vector?
• How do you convert a given vector into a unit vector?
• What are the standard notation symbols for unit vectors in Cartesian coordinates?

Related terms

Vector Magnitude: The length or size of a vector, calculated as the square root of the sum of the squares of its components.

Cartesian Coordinates: A coordinate system that specifies each point uniquely in a plane by a pair of numerical coordinates, which are distances from two fixed perpendicular directed lines.

\(\hat{i},\hat{j},\hat{k}\): Standard unit vectors in three-dimensional space representing directions along the x-axis, y-axis, and z-axis respectively.