CHAPTER 1 Mathematics

^Full Chapter Menu

Collinear Vectors

First we'll look at collinear vectors. (There's some disagreement on the number of l's in this word.) We'll do this using some interactive examples. There's no video here. You'll participate by using the gadgets that I've been demonstrating in the lessons.

In this example you'll try one graphical addition problem & then look more closely at addition of collinear vectors. Use a scale of 10:1. That is, a 15 cm vector will be drawn 150 pixels long.

Perpendicular Vectors

Another common situation occurs when two vectors act perpendicular to one another. This is an ideal case for the use of trigonometry.

Try your hand at this example.

Subtracting Vectors

The need to subtract vectors comes up in the same way as the need for subtracting scalars.

Scalars

Problem: You have $45 now and need to have $80. How much do you need to dig out of the couch cushions?

Solution:
Initial Cash + Added Cash = Final Cash
Added Cash = Final Cash - Initial Cash

Vectors

Problem: An ant walks 20 cm east, then walks in another straight line. If she is now

1. 30 cm east of her starting point, or
2. 30 cm west of her starting point, or
3. 30 cm northwest of her starting point

describe the second leg of her trip.

Solution:
First Displacement + Second Displacement = Resultant Displacement
Second Displacement = Resultant Displacement - First Displacement

The fact that these are all vectors makes the method of solution a bit more complex. Rather than defining a new process, vector subtraction, we'll make one modification and then use vector addition which we already know how to do. Here's the process.