Triple Vector Product

direction only

a

1

-1.58

a

2

0

a

3

3

b

1

2

b

2

-5.

b

3

2

c

1

2

c

2

2.28

c

3

0

The triple vector product

a×(b×c)

, which can also be written in the form

(a·c)b-(a·b)c

, is one way of multiplying the three vectors

a=(

a

1

,

a

2

,

a

3

)

,

b=(

b

1

,

b

2

,

b

3

)

,

c=(

c

1

,

c

2

,

c

3

)

. The result is a vector lying in the same plane as

b

and

c

. Here the vector triple product is shown in red, and the vector

b×c

is also shown in magenta. The blue plane is the plane determined by

b

and

c

, to which the magenta vector is perpendicular. You can choose to see the unit vector in the direction of

a×(b×c)

with "direction only".