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).

- First, determine the vectors A, B, and C.
- Next, calculate the dot product of A and C (A . C).
- Next, calculate the dot product of A and B (A . B).
- Next, calculate the cross product of B and C (B x C).
- Finally, calculate the Vector Triple Product using the formula: A x (B x C) = B(A . C) – C(A . B).
- 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)