Points
Points and vectors are different concepts.
A point is a fixed place in space.
A vector can be thought of as the motion between points.
A mentioned previously, we will distinguish between points and vectors in our notation.
Points are denoted as and
vectors as .
Furthermore, we will consider vectors to live in the linear space R3
and points to to live in the Affine space A3. Let's consider this distinction.
Conceptually, the operations of addtion and multiplication by a scalar are well
defined for vectors. The addition of 2 vectors expresses the concatenation of 2 motions.
Multipling a vector by some factor scales the motion.
However, these opereations don't make sense for points. What should it mean to
add to points together? For example, what is Cambridge plus Boston? What does it mean
to multiply a point by an arbitrary scalar? What is 7 times Brookline?
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