Vectors, dot product, and vector components

Main points:
• Scalar multiplication
○ multiply a vector by a constant to get another vector whose length is
rescaled by that constant

• Vector addition
○ add two vectors to get a vector

• Dot products
○ The dot product u·v of two vectors u and v is the real number obtained
by multiplying corresponding coordinates of the vectors and adding

• The length of a vector u
○ IuI=√u*u

• Angle 0 between two nonzero vectors u and u
○ u*v=IuIIuI cos0
• Projection of a vector on a line
• The vector xu is the projection of a on the line spanned by u

Challenges:
I have not done vectors for a while and even when I studied the topic year ago, it was the one area where I had difficulties. I can somehow understand the basic principles but applying my knowledge is where it becomes difficult. So finding whether vectors are parallel is something I have troubles with.

Reflection:

I am still wondering how to apply vectors in the real world, as the examples were just mathematical ones. I would like to see examples how to apply vectors to problems in economics or sciences. This would provide me more motivation and personal interest to master this topic.