Vector Triple Product Calculator

Vector Triple Product Formula:

\[ VTP = A \times (B \times C) \]

Vector A (x):

Vector A (y):

Vector A (z):

Vector B (x):

Vector B (y):

Vector B (z):

Vector C (x):

Vector C (y):

Vector C (z):

Vector Triple Product Result:

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1. What is the Vector Triple Product?

The vector triple product is a mathematical operation involving three vectors in three-dimensional space. It is defined as A × (B × C), where × denotes the cross product. This operation results in a vector that lies in the plane of B and C.

2. How Does the Calculator Work?

The calculator computes the vector triple product using the formula:

\[ VTP = A \times (B \times C) \]

Where:

A, B, C — Three-dimensional vectors
× — Cross product operation

Explanation: The calculation involves two cross product operations. First, we compute the cross product of B and C, then we compute the cross product of A with the result of the first operation.

3. Applications of Vector Triple Product

Details: The vector triple product has applications in physics, engineering, and computer graphics. It's used in torque calculations, angular momentum, and determining perpendicular components of vectors.

4. Using the Calculator

Tips: Enter the x, y, and z components for each of the three vectors A, B, and C. The calculator will compute the vector triple product A × (B × C) and display the result as a vector.

5. Frequently Asked Questions (FAQ)

Q1: What is the geometric interpretation of the vector triple product?
A: The result vector lies in the plane spanned by vectors B and C, and is perpendicular to vector A.

Q2: Is the vector triple product associative?
A: No, the vector triple product is not associative. A × (B × C) is generally not equal to (A × B) × C.

Q3: What's the relationship between vector triple product and scalar triple product?
A: They are different operations. The scalar triple product (A · (B × C)) gives a scalar value, while the vector triple product gives a vector.

Q4: Can the vector triple product be expressed in terms of dot products?
A: Yes, through the vector triple product expansion: A × (B × C) = B(A · C) - C(A · B).

Q5: In which fields is the vector triple product commonly used?
A: It's frequently used in physics (especially mechanics), engineering, computer graphics, and robotics for various vector operations and transformations.