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Degree: Mathematics (Bachelors) - Edinburgh University
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Vinita (Parent) March 16 2015
Vinita (Parent) March 9 2015
First, we need to recall 2 basic definitions of vector operations:
The dot product is defined on vectors u=[u1, u2,...un] and v=[v1, v2,..., vn] as u . v = u1v1+u2v2+...+unvn
The length (norm) of a vector v=[v1, v2,..., vn] is the nonnegative scalar defined as ||v||=√(v . v)=√(v12+v22+...+vn2)
Note that u & v must be the same size to compute the dot product.
Now the formula for the angle, θ, between 2 vectors is as follows:
cos(θ)=(u . v)/(||u|| ||v||)
Notice that u & v can be any size so long as they are both the same size. That is, this formula can be used to find the angle between vectors in 2 dimensions and also to find the angle between vectors in 100 dimensions, however hard that is to imagine.
A handy rearrangement of that formula to isolate θ is:
θ=cos-1( (u . v)/(||u|| ||v||) )