Unit Vector Calculator

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Calculate the unit vector (direction) of a given vector by normalizing its magnitude to 1.

Vector Definition

Normalized Vector

\hat{u} = \langle 0.6000, 0.8000 \rangle

Magnitude |v|5.0000

Check (|û|)1.0000

About this calculator

What is a Unit Vector?

A unit vector is a vector that has a magnitude (length) of exactly 1. It is often used to indicate direction. To find a unit vector û in the same direction as a vector v, you divide v by its magnitude |v|.

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Pro Tips

Normalization: The process of finding the unit vector is called normalization.
Notation: Unit vectors are often denoted with a 'hat' (e.g., î, ĵ, k̂ or û).
Direction Cosines: The components of a unit vector correspond to the cosines of the angles the vector makes with the coordinate axes.

Fun Facts

"The standard basis vectors i, j, k are all unit vectors."
"Unit vectors are crucial in computer graphics for calculating lighting and reflections."

Formula: \hat{u} = \frac{\vec{v}}{|\vec{v}|} = \left\langle \frac{x}{\sqrt{x^2+y^2+z^2}}, \frac{y}{\sqrt{x^2+y^2+z^2}}, \frac{z}{\sqrt{x^2+y^2+z^2}} \right\rangle