# Determining a point in 3D space

So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). The rotation around both the x and y-axis is 45 degrees. What are the (x,y,z) coordinates of the point which is 10 units away from the beginning coordinates? Sorry if that was confusing, but I didn't know how to word it.

Keep in mind, only rotation about the x and y axis, not the z axis.

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You don't have enough information: you need to know which direction from the beginning coordinates the point was. Just knowing that it was ten units away, it could have started anywhere on the sphere with radius ten and ended anywhere on the same sphere. If you know the starting coordinates of the point (not just that it's ten units away), then you can use rotation matrices to find its final position. –  Jonathan Christensen Dec 1 '12 at 23:59
I don't think I understand. I wish to find the point located 10 units away from this point and on the line which is angled at 45 degrees on the x and y axis. Doesn't the angle of view determine the direction from the beginning coordinate? –  MrDoctorProfessorTyler Dec 2 '12 at 0:06
I'm not sure what you mean by "angle of view," but it sounds to me like there isn't any rotation involved in this problem at all. You want the point which is ten units away from the origin on a line through the origin that is at some angle (45 degrees) with both the x-axis and the y-axis? By "no rotation about the z axis" do you mean that the line is in the xy plane? "Rotation" is a transformation that takes something from one location to another, so if that's not what's going on you should restate your question more clearly. –  Jonathan Christensen Dec 2 '12 at 0:14
"You want the point which is ten units away from the origin on a line through the origin that is at some angle (45 degrees) with both the x-axis and the y-axis?" Exactly. There is no rotation around the z axis so it can be considered 0. To clarify what I mean by rotation, this image shows rotation around each axis: f-lohmueller.de/pov_tut/trans/rotatet.gif –  MrDoctorProfessorTyler Dec 2 '12 at 0:20
Rotation only makes sense as a transformation from an initial position to another position. What is the initial position? –  Jonathan Christensen Dec 2 '12 at 0:36