How do you prove a triple product?

In a vector triple product, we learn about the cross product of three vectors….Vector Triple Product Properties

1. The vector triple product a × (b × c) is a linear combination of those two vectors which are within brackets.
2. The ‘r’ vector r=a×(b×c) is perpendicular to a vector and remains in the b and c plane.

Why scalar triple product is called Box product?

Properties of the scalar triple product. For any three vectors , and , ( × ) ⋅ = ⋅ ( × ) . For this reason and also because the absolute value of a scalar triple product represents the volume of a box (rectangular parallelepiped),a scalar triple product is also called a box product.

What are the properties of scalar triple product?

Scalar triple product properties

• Geometric interpretation.
• Geometric interpretation.
• If the mixed product of three non-zero vectors equal to zero, these vectors are coplanar.
• a · [b × c] = b · (a · c) – c · (a · b)
• a · [b × c] = b · [c × a] = c · [a × b] = -a · [c × b] = -b · [a × c] = -c · [b × a]

What does Vector triple product represent?

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.

Can you take a dot product of 3 vectors?

The scalar triple product of three vectors a, b, and c is (a×b)⋅c. It is a scalar product because, just like the dot product, it evaluates to a single number. (In this way, it is unlike the cross product, which is a vector.)

Can you dot 3 vectors?

So for performing the operation of dot product, we need two vectors and since a.b is a scalar , this result cannot be involved in a dot product with vector c. Thus, dot product of three vectors is not possible but cross product is possible.