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Conclusion
In this chapter, we developed the basic geometry of vectors in
\(\R^3\text{.}\)
Vector addition and scalar multiplication make it possible to combine directions and magnitudes algebraically.
The dot product measures length, angle, orthogonality, and projection.
The wedge product and cross product encode oriented area, while the triple product encodes signed volume and orientation.
Parameterizations describe curves and surfaces by vector-valued functions, giving concrete models for lines, planes, cylinders, spheres, and other geometric objects.
