[SOLVED] Linear Algebra Question, tilting plane angle? 1. The problem statement, all variables and given/known data A million years ago, an alien species built a vertical tower on a horizontal plane. When they returned they discovered that the ground had tilted so that measurements of 3 points on the ground gave coordinates of (0, 0, 0), (3, 1, 0), and (0, 2, 1). By what angle does the tower now deviate from the vertical? 2. Relevant equations cross product, dot product. 3. The attempt at a solution I'm pretty sure that I have the theory, what I'm not sure on is where the x, y and z axis are in relation to "horizontal" and "vertical". I'm thinking that to find the answer I need to use the normals of the planes (found by cross product of two vectors derived from points). I would then use a modified dot product formula to get the angle. The stumbling block I'm running into is assigning points (and therefor vectors and a plane) to the "horizontal plane" in the question, which (x, y, or z) is pointing "up". If I take z as the upward axis I get, Original plane: normal (0,0,1) Tilted plane: points, (0,0,0), (3,1,0), and (0,2,1), to get vectors (3,1,0), and (0,2,1). cross product to get normal of (1,-3, 6), use dot product to get that the angle must be (cos-1)(6/(sqrt(46)) Am I on the right track?? Edited to add, I am having trouble with some linear transformation problems too so have added them too. Thanks!! one has an attempted solution (wrong) the other I am completely stuck on but have the theory on the bottom right. 1. The problem statement, all variables and given/known data I'm not sure how to take the theory we learned and apply it to this question. 1. The problem statement, all variables and given/known data Attempted solution, is wrong. The original question reads.