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Level 16

Cross Product


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Cross Product
a × b = <a2b3-a3b2, a3b1-a1b3, a1b2-a2b1>
Orthogonal Vectors to Cross Product
a × b is orthogonal to both vectors a and b
|a × b|=|a||b|sin?
Angle between a and b
V=|a·(b×c)|
Volume of Parallelepiped
Property of Cross Product 1
a × b = -b × a
Property of Cross Product 2
(da) × b = d(a × b) = a × (db)
Property of Cross Product 3
a × (b+c) = a×b + a×c
Property of Cross Product 4
(a+b) × c = a×c + b×c
a·(b×c)=(a×b)·c
Property of Cross Product 5
a×(b×c)=(a·c)b-(a·b)c
Property of Cross Product 6
The length of their cross product |AB×BC|
Area of a Parallelogram with adjacent sides AB and BC