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## Main Question or Discussion Point

These problems are actually for my classical mechanics class, but they are linear-algebra based. I can construct a transformation matrix, but I have trouble visualizing the rotations, particularly in 3-space. So if someone could help me get a pictorial idea of what's actually happening, then the problems would be much easier!!!

1) Find the transformation matrix that rotates the x3 (z) axis of a regular coordinate system 45 degrees toward x1 (x) around the x2 (y) -axis.

Here's the matrix I got for this one:

1 0 0

0 1 0

sqrt2/2 -sqrt2/2 sqrt2/2

2) Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120 degrees about an axis making equal angles with the original three coordinate axes.

Here's the matrix I came up with for this one:

-.5 sqrt3/2 .5

.5 -.5 sqrt3/2

sqrt3/2 .5 -.5

Thanks!!!

1) Find the transformation matrix that rotates the x3 (z) axis of a regular coordinate system 45 degrees toward x1 (x) around the x2 (y) -axis.

Here's the matrix I got for this one:

1 0 0

0 1 0

sqrt2/2 -sqrt2/2 sqrt2/2

2) Find the transformation matrix that rotates a rectangular coordinate system through an angle of 120 degrees about an axis making equal angles with the original three coordinate axes.

Here's the matrix I came up with for this one:

-.5 sqrt3/2 .5

.5 -.5 sqrt3/2

sqrt3/2 .5 -.5

Thanks!!!