Can you reduce a vector triple product? i.e. (A x (uB x C))

In summary, a vector triple product is an operation involving three vectors, typically denoted as A, B, and C, where the result is a vector perpendicular to both A and the cross product of B and C. To calculate a vector triple product, the cross product of B and C is taken, followed by the cross product of A with the result. It is possible to reduce a vector triple product by using the properties of the cross product. Real-world applications of vector triple products include calculating moments of inertia and determining magnetic fields. An example of a vector triple product is (A x (B x C)), where A = [1, 2, 3], B = [4, 5, 6], and C =
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UAJalen
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My question is simply whether you can reduce a vector triple product, or more generally a scalar multiplier of a vector in a cross product?

Given: (A x (uB x C) = v, where u and v are known constants.

Is it valid to change that to: u(A x (B x C) = v

or
(A x uB) = v, can you change that to u(A x B) = v
 
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1. Can you explain what a vector triple product is?

Yes, a vector triple product is an operation that involves three vectors, typically denoted as A, B, and C. It is defined as the cross product of one vector (A) with the cross product of the other two vectors (B x C). The result is a vector that is perpendicular to both A and the cross product of B and C.

2. How do you calculate a vector triple product?

To calculate a vector triple product, you first need to take the cross product of B and C. Then, take the cross product of A with the result of the first cross product. The final result will be a vector that is perpendicular to both A and the cross product of B and C.

3. Is it possible to reduce a vector triple product?

Yes, it is possible to reduce a vector triple product by using the properties of the cross product. For example, the cross product is distributive, so you can rearrange the terms in the vector triple product to simplify the calculation.

4. What are some real-world applications of vector triple products?

Vector triple products have various applications in physics and engineering. For example, they are used in mechanics to calculate moments of inertia and in electromagnetism to determine the magnetic field generated by an electric current.

5. Can you provide an example of a vector triple product?

Yes, for example, if we have vectors A = [1, 2, 3], B = [4, 5, 6], and C = [7, 8, 9], the vector triple product would be (A x (B x C)) = (1, 2, 3) x [(4, 5, 6) x (7, 8, 9)]. By using the cross product properties, we can simplify this to (A x (B x C)) = (1, 2, 3) x (-3, 6, -3) = (-12, -6, 6).

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