Linear Algebra: 1.0, 1.1, 1.2, 4.1.0

Main Points
1.0
Coordinates can be represented by a vector which starts at the origin (0,0). The coordinates of a vecotr are written vertically, with the x-coordinate above the y. This shows that a vector is being used rather than just the point. a zero vector would simply be a point at the origin since both the head and tail of the vector are in the same place.
1.1
There are 2 operations that can be done with vectors and not points on a plane, one of which is scalar multiplication, where we multiply a vector (both the x and y coordinates) by a constant.
1.2
It is also possible to add two vectors together, called coordinate-wise addition (because corresponding coordinates are added, ie, x with x and y with y). This sum is represented as the diagonal of the parallelogram drawn with the original vectors on two sides.
4.2: Dot Products
Def: The dot product of two vectors is teh real number obtained by multiplying corresponding coordinates of the vectors and adding. Note that this is a single number, a scalar, not a vector. Also the product of 2 vectors is 0 if they are perpendicular to each other.

Challenges
Other than the benefits of having direction included, what are the benefits of having a vector to work with rather than just a point since its just the number that we are often using anyway?

Reflections
Again I can see how calculus applies to life as even with the plain examples that simply include graphs and vectors, I can connect them with problems about wind speed and how it would affect a travelling boat for example.