- published: 05 Sep 2012
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In vector calculus, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.
The scalar triple product (also called the mixed or box product) is defined as the dot product of one of the vectors with the cross product of the other two.
Geometrically, the scalar triple product
is the (signed) volume of the parallelepiped defined by the three vectors given. Here, the parentheses may be omitted without causing ambiguity, since the dot product cannot be evaluated first. If it were, it would leave the cross product of a scalar and a vector, which is not defined.
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I cover the scalar and vector triple products. https://www.youtube.com/playlist?list=PLDDEED00333C1C30E&feature;=view_all
A shortcut for having to evaluate the cross product of three vectors Watch the next lesson: https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/normal-vector-from-plane-equation?utm_source=YT&utm;_medium=Desc&utm;_campaign=LinearAlgebra Missed the previous lesson? https://www.khanacademy.org/math/linear-algebra/vectors_and_spaces/dot_cross_products/v/dot-and-cross-product-comparison-intuition?utm_source=YT&utm;_medium=Desc&utm;_campaign=LinearAlgebra Linear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two ...
This video explains how to determine the volume of a parallelepiped using the triple scalar product. http://mathispower4u.yolasite.com/
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This video describes the Scalar triple product of three vectors.Scalar triple product is the product of three vectors whose output is a scalar quantity.
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If three vector a ⃗ , b ⃗ and c ⃗ represents the three adjacent sides of a paralleopiped then their scalar triple product is the numerically volume of that parallelepiped.
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Example to make three vectors coplanar by using scalar triple product