Which of the following are true about the triple scalar product of three vectors A, B, C?
Understand the Problem
The question is asking for statements that are true regarding the triple scalar product of three vectors A, B, and C. The triple scalar product is defined as the scalar product of one vector with the cross product of the other two vectors, and the user likely seeks to determine the properties or characteristics related to it.
Answer
The scalar triple product is (A×B)⋅C, is a scalar, represents the volume of a parallelepiped, and is zero if vectors are coplanar.
True statements about the scalar triple product of three vectors A, B, and C include: (1) It is given by (A×B)⋅C. (2) It is a scalar quantity. (3) It represents the volume of a parallelepiped formed by A, B, and C. (4) If it is zero, then the vectors are coplanar.
Answer for screen readers
True statements about the scalar triple product of three vectors A, B, and C include: (1) It is given by (A×B)⋅C. (2) It is a scalar quantity. (3) It represents the volume of a parallelepiped formed by A, B, and C. (4) If it is zero, then the vectors are coplanar.
More Information
The scalar triple product can also be cyclic, meaning the order of the vectors in the product does not change the result: (A×B)⋅C = (B×C)⋅A = (C×A)⋅B.
Sources
- The scalar triple product - Math Insight - mathinsight.org
- Scalar Triple Product - Formula, Geometrical Interpretation ... - cuemath.com
- Triple product - Wikipedia - en.wikipedia.org
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