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

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It is possible to find the cross product vector VxW using the magnitude of both vectors, the angle between them, and the plane they lie in. The formula for the magnitude of the cross product is Mag(VxW) = Mag(v) * Mag(w) * sin(theta), but isolating the actual vector requires additional information. The orientation of the cross product is determined by the right-hand rule, which depends on the direction of the vectors in the specified plane. There may be sign ambiguity related to the angle, which can affect the direction of the resulting vector. Overall, while the magnitude can be calculated, determining the exact vector requires careful consideration of the vectors' orientations.
Christie
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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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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.
 
What would b that ambiguity?
 

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