# Length/unit vector

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• April 22nd 2009, 04:46 PM
laser
Length/unit vector
For vector v=<3,2,-4>, how do you find the length and the unit vector in the same direction?
• April 22nd 2009, 04:54 PM
Gamma
Norm
All you gotta do is divide the vector by its length.

$|\vec{v}|=(\vec{v} \cdot \vec{v})^{1/2}$

So for any vector $\vec{v}$, you know that $\frac{\vec{v}}{|\vec{v}|}$ is a vector of unit length in the same direction as $\vec{v}$ you just multiplied it by a scalar to adjust its length to be 1.