Angle Between Vectors

Topics: Geometry - Linear Algebra

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(definition)

Given two vectors $u$ and $v$, the angle between them is given by:

$$\cos \theta =\frac{u\cdot v}{\Vert u\Vert \Vert v\Vert }$$

…with $\cdot$ denoting the traditional dot product (inner product).

(theorem)

Notice that $u$ and $v$ are orthogonal when $v\cdot w=0$.