Rotating a 3 coordinate point

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Im having trouble figuring out how to rotate the z axis 90 degrees. For a programming im making

example new_x = y; // For a 90 degree clockwise rotation, the new x is the original y, new_y = -x; // and the new y is -1 times the original x. So what would Z be. If its not to clear please let me know.

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A vector $(x,y,z)$ rotated about z 90° is $(-y,x,z)$