How can a rectangle be rotated in three dimensions?

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A rectangle can be rotated in three dimensions by specifying the angle of rotation and the axis of rotation. The rotation can be performed using a rotation matrix or quaternion.

To rotate a rectangle around the x-axis, for example, we can use the following rotation matrix:

[1 0 0 0 cos θ -sin θ 0 sin θ cos θ]

where θ is the angle of rotation.

To rotate a rectangle around the y-axis, we can use the following rotation matrix:

[cos θ 0 sin θ 0 1 0 -sin θ 0 cos θ]

To rotate a rectangle around the z-axis, we can use the following rotation matrix:

[cos θ -sin θ 0 sin θ cos θ 0 0 0 1]

Given a rectangle in 3D space with vertices (x1,y1,z1), (x2,y2,z2), (x3,y3,z3), and (x4,y4,z4), we can rotate it by multiplying each vertex by the appropriate rotation matrix.