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
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.
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.
