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