# Triple Vector Product

Triple Vector Product

The triple vector product , which can also be written in the form , is one way of multiplying the three vectors , , . The result is a vector lying in the same plane as and . Here the vector triple product is shown in red, and the vector is also shown in magenta. The blue plane is the plane determined by and , to which the magenta vector is perpendicular. You can choose to see the unit vector in the direction of with "direction only".

a×(b×c)

(a·c)b-(a·b)c

a=(,,)

a

1

a

2

a

3

b=(,,)

b

1

b

2

b

3

c=(,,)

c

1

c

2

c

3

b

c

b×c

b

c

a×(b×c)