>The current topic is scalar product and vector product. I can use scalar >product to find the angle between two vectors that are given in Cartesian >form. But that's not really an application, of itself. I also know that >scalar product is used to calculate the work done (magnitude of displacement >by the magnitude of the component of the force in the direction of the >displacement). Does anyone have any other examples/applications of scalar >product, suitable for a high school class? > >Ditto for vector product. The text isn't much help - it uses vector product >to find the area of a triangle and poses a question at the end of an exercise >set - find a real-world problem whose solution involves a vector product. > >Thanks in advance for any assistance. > >Rex >-- >
Of course, any reasonable classical mechanics book gives load of examples. Some of which might be suitable for a high school class and some not. But I had ( and still do amazingly enough) an nice little book by G. E. Hays published by Dover which I always liked. It is called Vector and Tensor Analysis and does a few theorems in plane geometry, solid, and differential and then has some applications to mechanics. Then it gets a bit deep. Just glancing there are two theorems in pl g: Diags of parallelogram bisect each other and the medians of a tri meet in a single point which trisects each of them. Of course, all done with vectors. However, glancing at the proofs no products.
But the solid discussion uses products for area of a triangle (as you noted), equations of lines and planes and tangent planes. If you have every done this with good old sines and cosines, you really appreciate the vector method.