Enter the vectors and their respective cross or dot products into the calculator to determine the vector triple product.

Vector Triple Product Formula

The following formula is used to calculate the vector triple product. 

A x (B x C) = B(A . C) - C(A . B)

Variables:

  • A, B, C are vectors
  • x is the cross product operator
  • . is the dot product operator

To calculate the vector triple product, first calculate the cross product of vectors B and C. Then, calculate the dot product of vector A with the result of the cross product. This forms the first term of the equation. For the second term, calculate the dot product of vector A with vector B, and then multiply the result with vector C. Finally, subtract the second term from the first term to get the vector triple product.

What is a Vector Triple Product?

The Vector Triple Product is a mathematical operation in vector algebra that involves the cross-product of three vectors. It is expressed as A × (B × C), where A, B, and C are three vectors. The result of this operation is a new vector that is perpendicular to the plane defined by the original three vectors. The magnitude and direction of this new vector are determined by the right-hand rule. The Vector Triple Product has the property of not being associative, meaning that (A × B) × C does not necessarily equal A × (B × C).

How to Calculate Vector Triple Product?

The following steps outline how to calculate the Vector Triple Product using the formula: A x (B x C) = B(A . C) – C(A . B).

  1. First, determine the vectors A, B, and C.
  2. Next, calculate the dot product of A and C (A . C).
  3. Next, calculate the dot product of A and B (A . B).
  4. Next, calculate the cross product of B and C (B x C).
  5. Finally, calculate the Vector Triple Product using the formula: A x (B x C) = B(A . C) – C(A . B).
  6. After inserting the values of A, B, and C into the formula and performing the calculations, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge:

A = (2, 3, 4)

B = (5, 6, 7)

C = (8, 9, 10)