Enter the vectors A, B, and C into the scalar triple product calculator.
Scalar Triple Product Formula
The scalar triple product calculator formula is used to calculate the scalar triple product of three vectors.
STP = (A · (B × C))
Variables:
- STP is the scalar triple product
- A, B, and C are the three vectors
To calculate the scalar triple product, first calculate the cross product of vectors B and C. Then, take the dot product of vector A with the result of the cross product.
What is a Scalar Triple Product?
The Scalar Triple Product, also known as the Box Product, is a mathematical operation involving three vectors in three-dimensional space. It is denoted as [a, b, c] or (a·(b×c)) and results in a scalar (a single real number). The operation is a combination of the dot product and the cross product. First, the cross product of two vectors (b and c) is calculated, resulting in a new vector. Then, the dot product of the first vector (a) and this new vector is calculated, resulting in a scalar. The scalar triple product has the geometric interpretation as the volume of the parallelepiped spanned by the three vectors. It is zero if and only if the three vectors are coplanar, implying that they lie in the same plane.
How to Calculate Scalar Triple Product?
The following steps outline how to calculate the Scalar Triple Product.
- First, determine the three vectors involved: A, B, and C.
- Next, calculate the cross product of vectors A and B.
- Then, take the dot product of the resulting cross product and vector C.
- Finally, calculate the Scalar Triple Product.
- After inserting the vectors and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following vectors as an example problem to test your knowledge:
Vector A = (2, 3, 4)
Vector B = (5, 6, 7)
Vector C = (8, 9, 10)
