Triple Vector Product

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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".

Contributed by: Roberta Grech (August 2013)
Open content licensed under CC BY-NC-SA



Snapshot 1: both magnitude and direction of the triple vector product

Snapshot 2: and are parallel

Snapshot 3: and are perpendicular

The triple vector product for non-zero vectors , , vanishes when is parallel to or is parallel to .


[1] D. Fleisch, A Student's Guide to Vectors and Tensors, New York: Cambridge University Press, 2012.

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