       Solve & RotationMatrix

• To: mathgroup at smc.vnet.net
• Subject: [mg75836] Solve & RotationMatrix
• From: gentilemathieu at gmail.com
• Date: Fri, 11 May 2007 06:20:04 -0400 (EDT)

```Hello,

\[Alpha] =.; \[Beta] =.; \[Gamma] =.;
VectX = {1, 0, 0};
VectY = {0, 1, 0};
VectZ = {0, 0, 1};
RotX = RotationMatrix[\[Alpha], VectX];
RotY = RotationMatrix[\[Beta], VectY];
RotZ = RotationMatrix[\[Gamma], VectZ];
Rotation = RotX.RotY.RotZ;
PtO = {0, 0, 0};
PtA = {1, 0, 0};
PtB = {0, 1, 1};
VectN = Normalize[Cross[PtA - PtO, PtB - PtO]];
Solve[VectN == Rotation.VectY, {\[Alpha], \[Beta], \[Gamma]}]

I have a crystal with a face on which I can measure the XYZ
coordinates of 3 points PtO, PtA, PtB.
>From these I compute the vector normal to the surface.

I would then like to compute the Alpha, Beta, Gamma rotation angles
about the x, y and z axis respectively as compared to the ideal
position for which the crystal face would lie in the XZ plane, i.e.
its normal vector being the y axis.

Thank you,
Best regards,
Mathieu

```

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