Vectors

Why Study Vectors?

You use vectors in almost every activity you do. A vector is a quantity that has size and direction. The fancy word for size is "magnitude".

Examples of everyday activities that involve vectors include:

• Breathing (your diaphragm muscles exert a force that has a magnitude and direction)
• Walking (you walk at a velocity of around 6 km/h in the direction of the bathroom)
• Going to school (the bus has a length of about 20 m and is headed towards your school)
• Lunch (the displacement from your class room to the canteen is about 40 m in a northerly direction)

Each vector quantity has a magnitude and a direction.

In this Chapter

We start slow and easy by talking about simple vectors:

• How to write and draw vectors
• Adding one-dimensional Vectors

Next, we move on to 2-dimensional vectors

• Two-dimensional Vectors
• Adding 2-dimensional vectors
• Dot product of 2-dimensional vectors

Next up is the interesting 3-D stuff:

• 3-dimensional space
• Vectors in 3-D space
• Cross product of vectors

To round out this chapter, we talk about

• Vectors that vary as time goes on
• Vector calculus

So let's start with Vector Concepts and Notation.