Vector cross product with coefficients

Thread starter Stickybees
Start date Oct 1, 2012
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In summary, a vector cross product with coefficients is a mathematical operation that produces a third vector perpendicular to two original vectors. It is calculated using a formula involving determinants and has significant applications in physics, engineering, and computer graphics. It can only be calculated for two vectors in three-dimensional space, but multiple cross products can be performed for more than two vectors.

Oct 1, 2012

Stickybees

Anyone know how would I simplify a cross product where the two vectors have coefficients? For example [itex](x/(y^3))\bar{r}[/itex] X [itex](x/(y))\bar{L}[/itex]

Thanks!

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Oct 1, 2012

Muphrid

Just pull the coefficients out.

Oct 1, 2012

HallsofIvy

Science Advisor

Homework Helper

In other words, [itex](a\vec{u})\times(b\vec{v})= ab (\vec{u}\times \vec{b})[/itex].

Related to Vector cross product with coefficients

1. What is a vector cross product with coefficients?

A vector cross product with coefficients is a mathematical operation performed on two vectors to produce a third vector that is perpendicular to both of the original vectors. Coefficients, or scalars, are used to scale the magnitude of the resulting vector.

2. How is the vector cross product with coefficients calculated?

The vector cross product with coefficients is calculated using the cross product formula, which involves taking the determinant of a 3x3 matrix composed of the components of the two original vectors. This results in a new vector with three components.

3. What is the significance of the direction of the resulting vector in a cross product?

The direction of the resulting vector in a cross product is significant because it is perpendicular to the plane formed by the two original vectors. This can be used to determine the orientation of an object or the direction of a force in a given system.

4. Can the vector cross product be calculated for more than two vectors?

No, the vector cross product is only defined for two vectors in three-dimensional space. However, multiple cross products can be performed to find the resulting vector of more than two vectors.

5. What are some applications of the vector cross product with coefficients?

The vector cross product with coefficients is commonly used in physics and engineering to calculate torque, angular momentum, and magnetic fields. It is also used in computer graphics and 3D modeling to determine the orientation of objects and to create realistic lighting effects.