The Dot Product
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Property 4 of Dot Product
(xa)∙b=x(a∙b)=a∙(xb) x is a scalar
Property 5 of Dot Product
0∙a=0 (First zero is the zero vector and the second is the numerical value zero)
Property 3 of Dot Product
a∙(b+c)=a∙b+a∙c
Property 1 of Dot Product
a∙a=|a|²
Determining orthogonal vectors
a∙b=0
Dot Product
a∙b=a₁b₁+a₂b₂+a₃b₃
Property 2 of Dot Product
a∙b=b∙a
Angle between Vectors
a∙b=|a||b|cosΘ cosΘ=(a∙b)/(|a||b|)
Scalar Projection of b onto a
comp_a b=(a∙b)/|a|
Vector Projection
proj_a b=a(a∙b)/|a|²