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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