Products of Vectors
In Chapter 12, we saw that vectors can be used to study points and lines in three dimensional space. Another fundamental concept in geometry that was not considered there is angle. In this chapter we define the angle between vectors. In connection with this we introduce the scalar product of vectors.
We also study a second product, the vector product. Both products have many properties which resemble those familiar properties of the product of real numbers. However the vector product is not commutative.
Whereas the scalar product is often used to compute angles, one purpose of the vector product is to construct a vector perpendicular to two given vectors. This property is used in solving problems related to planes ...
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