Dot product

Dot product: used to compute projections, angles and lengths.

Notation: (w,v) = dot product of vectors w and v.

a

w

v

(w,v) = |w| |v| cosa,

|v| = length of v

Properties:

if w and v are perpendicular, (w,v) = 0

(w,w) = |w|2

angle between w and v: cosa = (w,v)/|w||v|

length of projection of w on v: (w,v)/|v|

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