Enter any vector into the normalize vector calculator. The calculator will normalize this vector and display the unit vector.

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## Normalizing a Vector Formula

The following formula is used to normalize a vector.

u = U / |U|

|U| = Square Root ( X^2 + Y^2+Z^2)

- Where U is the original vector
- |U| is the magnitude of the vector
- u is the unit vector

## Normalize Vector Definition

A vector normalization is a process of finding the unit vector of a given vector.

## How to normalize a vector?

How to normalize a vector?

**First, calculate the magnitude of the original vector**Using the formula above, calculate the magnitude of the original vector.

**Next, divide each component of the vector by the magnitude.**For example, for a vector x,y,z, divide x by the magnitude, y by the magnitude, and z by the magnitude. The results of those divisions are your unit vector values.

**Example Problem: **

In the following example, a vector of (5,6,10) is given.

First, the magnitude of the vector must bed calculated. Using the formula above:

|U| = sqrt( 5^2 + 6^2+10^2)

|U| = 12. 688

Next, divide each individual component of the vector by the magnitude to normalize the vector.

X = 5 / 12.688 = .394

Y = 6 / 12.688 = .472

Z = 10 / 12.688 = .788

So the final normalized vector would be (.394,.472,.788).

## FAQ

**What is normalizing a vector?**

Normalizing a vector is the process of turning a vector into its unit vector. This process involves dividing a vector by its magnitude. The result is a vector with the same direction, but with a magnitude of 1.

**Why would you normalize a vector?**

Normalizing a vector can simply problems. For example, if you want to multiply two vectors A and B, you can actually multiply their unit vectors to get the direction, then multiply that answer by the magnitudes to get the resulting vector of A * B.