Since translation doesn't affect directions, the direction vectors f and g change to ABC f and ABC g respectively. Note that the transformation always works on the initial position and direction vectors, using the current values of A, B, C and v . While you could enter any linear transformations for A, B and C, it's a very bad idea to try to stretch or shrink the airplane, so you should make sure that you only use rotations, which always keep distances constant. Here are some useful formulas for rotations about the x, y and z axes. Save your answers before leaving this page.
Saving is the same as submitting.
Only your last submission counts, although all are stored. Unfortunately, in this version of the submission procedure, you cannot reload any submission other than the last one. In principle, you should be able to submit your answers from home, but we cannot guarantee success in this. In case you have no success in submitting from anywhere else, you will have to submit from the Mathematics Department system. Send us e-mail .