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quantumfoam

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In summary, the conversation discusses the cross product of a constant vector and a vector, with one person asking if there is a formula for this product. The other person clarifies that the concept of "constant" or "variable" does not apply to the cross product, and talks about how to calculate it. The conversation ends with an apology for any confusion caused by the question.

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quantumfoam

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JonDrew

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To cross two vectors you can simply take the determinate of the matrix they make. As far as I know this method works for all constant and variable vectors which have a determinate that exist.

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HallsofIvy

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What do youquantumfoam said:

And what question are you referring to with "now that my question has been cleared up"? This is

- #4

quantumfoam

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The cross product of a constant vector is a mathematical operation that takes two vectors as inputs and produces a third vector that is perpendicular to both input vectors. It is also known as the vector product and is denoted by a cross (×) symbol.

The cross product of two vectors, *a* and *b*, is calculated using the following formula: *a* × *b* = |*a*| |*b*| sin(*θ*) *n*, where |*a*| and |*b*| are the magnitudes of the vectors, *θ* is the angle between them, and *n* is the unit vector perpendicular to both *a* and *b*.

The cross product has several important applications in physics, engineering, and computer graphics. It is used to calculate torque in physics, determine the direction of a magnetic field, and perform 3D rotations and transformations in computer graphics.

The cross product of two vectors is equal to zero when the vectors are parallel or antiparallel. This means that the vectors are either pointing in the same direction (parallel) or in opposite directions (antiparallel). In both cases, the angle between the vectors is either 0° or 180°, resulting in a zero value for the cross product.

One common misconception is that the cross product is commutative, meaning that the order of the vectors does not matter. However, the cross product is not commutative, and switching the order of the vectors will result in a different output vector. Another misconception is that the cross product of two vectors always produces a vector that is perpendicular to both input vectors. This is only true if the two vectors are not parallel or antiparallel.

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