Calculating the Cross Product Vector: Is It Possible to Find VxW?

In summary, the conversation is about finding the actual cross product vector, not just its magnitude, using information such as the magnitude of both vectors, the angle between them, and the plane they lie in. The formula for calculating the magnitude of the cross product is mentioned, but the person is wondering if there is a way to isolate the cross product vector from this information. There is also a mention of a possible sign ambiguity depending on the known angle.
  • #1
Christie
4
0
Okay so, I am wondering if it is possible to find the actual cross product (not the magnitude of the cross product) from this information
1. magnitude of both vectors
2.angle between vectors
3.plane the vectors lie in
Is there any way to calculate that cross product vector?
Thank you very much.
I know that
Mag (VxW)= Mag(v)Mag(w)sinthea
but am wondering if there is anyway to actually isolate VxW from this information.
 
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  • #2
It is the normal vector of the plane that has the appropriate magnitude.

Depending on what you mean by saying that the angle is known, there may or may not be a possible sign ambiguity.
 
  • #3
What would b that ambiguity?
 

What is a cross product?

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

How is the cross product calculated?

The cross product is calculated by taking the magnitudes of the two input vectors and multiplying them together, then multiplying by the sine of the angle between the two vectors.

What is the significance of the cross product magnitude?

The magnitude of the cross product is equal to the area of the parallelogram formed by the two input vectors. This can be useful in determining the orientation and size of a 3D shape.

Can the cross product be negative?

Yes, the cross product can be negative if the angle between the two input vectors is greater than 90 degrees. This indicates that the resulting vector is pointing in the opposite direction from what is expected.

What is the difference between a cross product and a dot product?

The main difference between a cross product and a dot product is the type of result they produce. A dot product results in a scalar, while a cross product results in a vector. Additionally, the dot product is commutative, meaning the order of the input vectors does not matter, while the cross product is not commutative.

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