Course Material

 

1. The following picture illustrates the addition of two-dimensional vectors. The resulting vector is in blue. The dotted lines are just so that we can see the coordinates of the resulting vector in terms of the two vectors that we add.

Here it is again, but this time without the doted lines.

Once again, this time to see that we can use a vector representative of one of the green vectors to get the same result.

2. An example illustrating addition of 3 dimensional vectors. (This is an interactive graphics. Please wait for the applet to load then drag to move the picture.)

3. The dot product of vectors. (This is a low quality animation - good enough to see. The signed length (could be negative) of the blue line is the dot product of the red and the green vector. As the red vector moves, the dot product changes too. The dot product is zero when the red and the green vectors are perpendicular.)

4. The vector product of vectors.(The blue vector is a cross product of the red and green vector. Note that the cross product is zero when the red and the green vector are colinear.)

5. The following two pictures provide visual solutions to Problem 19 and Problem 20 in Section 2.3. Each of the equations in the linear systems represents a plane in 3 dimensions. The solutions is their common intersection (in red).