Why is the z-axis perpendicular to the other axes?

Z-axis perpendicularity to the other two (mutually perpendicular) axes permits the simple distance-between-two-points formula to be used. That is, if A = (x1, y1, z1) and B = (x2, y2, z2), then the distance from A to B is sqrt((x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2). read more

The x, y and the z Axis are perpendicular just to provide a frame of reference..if you are comfortable then you can make your own reference frame, but then you would have to explain that frame first almost all the time because the x, y, z axis frame is accepted world-wide. read more

Given: One axis in an arbitrary-basis 3D coordinate system. There is not enough information to find the unique solution this problem. This is because, if you look at the second case (One axis in an arbitrary-basis 2D coordinate system), you first need to find an orthogonal vector. read more