The Cross Product of Three Vectors Calculator is a handy tool that allows users to compute the vector triple product of three given vectors. This calculation involves the manipulation of vectors A, B, and C, as denoted by the formula: A × (B × C). By inputting the values of these vectors into the calculator, users can quickly determine the resulting vector.
Formula of Cross Product of Three Vectors Calculator
The vector triple product of vectors A, B, and C, denoted by A × (B × C), can be calculated using the following formula:
Here, A ⋅ B represents the dot product of vectors A and B. This formula essentially multiplies vector B by the scalar quantity (A ⋅ C) and subtracts the result of multiplying vector C by the scalar quantity (A ⋅ B). The final output is a new vector.
Table of General Terms
| Term | Definition |
|---|---|
| Cross Product | A mathematical operation that multiplies two vectors in 3D space to produce a new vector, perpendicular to both original vectors. |
| Vector Triple Product (A × (B × C)) | A specific type of cross product involving three vectors. It’s calculated as B(A . C) – C(A . B), where the dot product (.) multiplies the corresponding components of two vectors and sums the products. |
| Dot Product | An operation that multiplies the corresponding components of two vectors and sums the products, resulting in a scalar quantity. |
| Three-Vector Cross Product Calculator | A digital tool that applies the vector triple product formula (A × (B × C)) to calculate a new vector based on three input vectors. |
Example of Cross Product of Three Vectors Calculator
Let’s consider an example to better understand how the Cross Product of Three Vectors Calculator works:
Suppose we have three vectors:
- Vector A = [3, 1, 2]
- Vector B = [2, 4, 6]
- Vector C = [1, 2, 3]
By applying these values to the calculator, we can compute the cross product of the three vectors.
Most Common FAQs
A: A vector is a mathematical quantity that has both magnitude and direction. In essence, it represents a displacement or change in position.
A: The dot product of two vectors is the result of multiplying the corresponding entries of the vectors and then summing them up. It yields a scalar quantity.
A: The calculator computes the vector triple product of three given vectors using the provided formula. It multiplies one vector by the dot product of the other two vectors and subtracts the result of multiplying another vector by the dot product of the remaining vectors.
