Definition:Unit Vector

Definition

A unit vector is a vector quantity which has a magnitude of $1$.

Dimension

The unit vector has no dimension.

This is because it consists of a quantity (of a dimension $D$) divided by another instance of that same quantity (also of dimension $D$), leaving no dimension.

Also see

• Unit Vector in Direction of Vector

• Results about unit vectors can be found here.

Sources

• 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $3$. Definitions of terms
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: Fundamental Definitions: $4.$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): unit vector
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): vector
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): unit vector
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): vector
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): unit vector