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Level 14

Dot Product


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a·b=a1b1+a2b2+a3b3
Dot Product
a·a=|a|²
Property 1 of Dot Product
a·b=b·a
Property 2 of Dot Product
a·(b+c)=a·b+a·c
Property 3 of Dot Product
(xa)·b=x(a·b)=a·(xb)
Property 4 of Dot Product
0·a=0
Property 5 of Dot Product
a·b=|a||b|cosT
Angle between Vectors
a·b=0
Determining orthogonal vectors
comp_a b=(a·b)/|a|
Scalar Projection of b onto a
Vector Projection
proj_a b=a(a·b)/|a|²