The Cross Product
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Property of Cross Product 4
(a+b) × c = a×c + b×c
Property of Cross Product 2
(da) × b = d(a × b) = a × (db) d is a scalar
Parallel Vectors
1) if they are a multiple of each other like <1,2,3> and <2,4,6> 2) if a × b=0
Angle between a and b
|a × b|=|a||b|sinθ sinθ=|a × b|/(|a||b|)
Volume of Parallelepiped
V=|a∙(b×c)|
Property of Cross Product 3
a × (b+c) = a×b + a×c
Property of Cross Product 1
a × b = -b × a
Cross Product
a × b = <a₂b₃-a₃b₂, a₃b₁-a₁b₃, a₁b₂-a₂b₁> (If you are like me, I just use the determinants of order 3 to obtain this)
Orthogonal Vectors to Cross Product
a × b is orthogonal to both vectors a and b
Property of Cross Product 6
a×(b×c)=(a∙c)b-(a∙b)c
Property of Cross Product 5
a∙(b×c)=(a×b)∙c
