The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two.

According to this figure, the three vectors are represented by the coterminous edges as shown. The cross product of vectors a and b gives the area of the base, and also, the direction of the cross product of vectors is perpendicular to both the vectors.

Scalar triple product is the dot product of a vector with the cross product of two other vectors, i.e., if a, b, c are three vectors, then their scalar triple product is a · (b × c). It is also commonly known as the triple scalar product, box product, and mixed product.

Using a scalar triple product formula, we combine the cross product of two of the vectors and the dot product of one of the vectors. We can write it as follows: abc= (a x b).c. This formula indicates the volume of a parallelepiped with three coterminous edges, for example, a, b, and c.

Apr 3, 2025 · The scalar triple product of three vectors A, B, and C is denoted [A,B,C] and defined by [A,B,C] = A·(BxC) (1) = B·(CxA) (2) = C·(AxB) (3) = det(ABC) (4) = |A_1 A_2 A_3; B_1 B_2 B_3; C_1 C_2 C_3| (5) where A·B denotes a dot product, AxB denotes a cross product, det(A)=|A| denotes a determinant, and A_i, B_i, and C_i are components of the ...

Vector Triple Product is a branch in vector algebra where we deal with the cross product of three vectors. The value of the vector triple product can be found by the cross product of a vector with the cross product of the other two vectors. It gives a vector as a result.

Apr 3, 2025 · The vector triple product identity is also known as the BAC-CAB identity, and can be written in the form Ax (BxC) = B (A·C)-C (A·B) (1) (AxB)xC = -Cx (AxB) (2) = -A (B·C)+B (A·C). (3)

Some other names for scalar triple product are mixed product and box product. It is used to determine the value of a parallelepiped’s volume where the given 3 vectors (a,b,c) denote a parallelepiped’s adjacent sides. We can draw the outcomes below based on the formula mentioned above:

In each case, decide whether AxB points up, down, left, right, into the page, or out of the page. The symbol means a vector pointing out of the page, and a vector pointing into it. B is a number and A × B results in a new vector. Also, when the magnitude of the dot product is a maximum, the magnitude of the cross-product is zero and vice versa.

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