Understanding Cross Product: A Refresher for 3(A x B) Calculation

Thread starter camino
Start date Sep 22, 2009
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Cross Cross product Product

In summary, a cross product is a mathematical operation that takes two vectors as inputs and produces a third vector that is perpendicular to both of the input vectors. It is calculated using a specific formula and has a geometric interpretation of producing a vector perpendicular to the input vectors. Some applications of cross products include calculating torque, magnetic force, and angular momentum, as well as in 3D graphics for determining surface direction and lighting effects. However, it can only be used with three-dimensional vectors as higher dimensions can result in an infinite number of perpendicular vectors.

Sep 22, 2009

camino

Homework Statement

I simply forget how to cross product if you have:

3(A x B)

Would it be 3A x B

or

A x B then take that result and multiply by 3?

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Sep 22, 2009

rock.freak667

Homework Helper

r(axb) = (ra)xb = ax(rb)

I believe it works like that for r=constant.

Sep 22, 2009

camino

Thank you that was my original thought.

1. What is a cross product?

A cross product is a mathematical operation that takes two vectors as inputs and produces a third vector that is perpendicular to both of the input vectors.

2. How is a cross product calculated?

To calculate the cross product between two vectors, you can use the following formula: A x B = (Ay * Bz - Az * By, Az * Bx - Ax * Bz, Ax * By - Ay * Bx), where A and B are the two input vectors and Ax, Ay, Az, Bx, By, Bz are their corresponding components.

3. What is the geometric interpretation of a cross product?

The geometric interpretation of a cross product is that it produces a vector that is perpendicular to both of the input vectors, and the direction of the resulting vector is determined by the right-hand rule.

4. What are some applications of cross products?

Cross products have many applications in physics, engineering, and computer graphics. They are used to calculate torque, magnetic force, and angular momentum, and are also used in 3D graphics to determine the direction of surfaces and to create realistic lighting effects.

5. Can the cross product be used with non-three-dimensional vectors?

No, the cross product is only defined for three-dimensional vectors. This is because the resulting vector is perpendicular to both input vectors, and in higher dimensions, there can be an infinite number of vectors perpendicular to two given vectors.