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Math Help - Three Dimensional Space

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    Junior Member Mrdavid445's Avatar
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    Three Dimensional Space

    In a three dimensional space, consider the point (x,y,z)=(4,3,1). Rotate this point 45 degrees counter-clockwise about the z-axis (as viewed from above). What are the coordinates of the new point?
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    GJA
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    Re: Three Dimensional Space

    Hi, Mrdavid445.

    Since the rotation is about the z-axis, we are rotating the point (4,3,1) in the plane z=1. Since the rotation occurs in a plane, we can use the two-dimensional counterclockwise rotation matrix

    R=\begin{pmatrix}<br />
\cos\theta & -\sin\theta\\<br />
\sin\theta & \cos\theta<br />
\end{pmatrix},

    where \theta is the angle of rotation - see Rotation matrix - Wikipedia, the free encyclopedia. If we multiply the vector [4,3]^{T} (T is the transpose) times the rotation matrix (after plugging in a value for \theta) we will obtain the new x and y coordinates for the rotated point. Since the rotation is in the plane z=1, the z coordinate will still be 1.

    Does that answer your question?

    Good luck!
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