Math Forum Discussions

Ed Wall

Posts: 36
Registered: 12/3/04

Re: scalar product and vector product
Posted: Jan 31, 1996 11:34 PM

Plain Text

>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.

Ed Wall