Graphical Vectors

Graphical Vectors

Back to vectors

When we draw vectors, their length should be proportional to the magnitude and its direction specific.

Naming Vectors

We can name vectors in two ways, we can define them as they go from one point to another, or by translating that to the origin and naming it with respect to the origin.

Unlike in coordinate geometry, these vectors do not represent points, but a motion along that direction relative to all other directions.

So how can we add vectors?

Well choose two vectors

Draw both these vectors with their ends on the origin

Translate one of these vectors so its tail is at the point,

where the other vectors head stops.

Now draw a new vector from the origin to the head of the added vector

(to the arrow is pointing away from the origin), simple really

If you dont get that try this.

Alternative Parallelogram Method

When it comes to less convieniently drawn vectors follow the following

While leaving the 1st vector where it is from its head (the arrow tip) draw a line Parallel to the other vector in the direction of the 2nd vector and having the same length as the 2nd vector

Now draw a line from the origin (the starting point for both vectors) to the tip of the copied vector, this is the resultant of the two vectors.

If you are unsure about these instructions, what you should do then follow this link to Walter Fendts site.

http://www.walter-fendt.de/ph14e/resultant.htm

Remarks on combining vectors

What if we go back to A from B ..... BA

If we add AB + BA ... or BA + AB

we go from A to B and back to A again

or from B to A and back to B again ... this is no distance therefore

AB + BA = 0 = BA + AB

or

AB = - BA

To add - the vectors should be in order (tail of one touching the tip of another) and

To subtract - the vectors should be in improper order (tails of the two vectors or tips of the two vectors should be touching each other

the vectors are expressed as from one point to another, like AB

Multiples of Vectors

A multiple of a vector will maintain the same direction. The Multiple only defines the magnitude (size) of the vector,

The Null Vector

This is the vector that has no magnitude and therefore no need for direction.

No matter how you do it you get the same result ................

Copy out the vectors above accurately on to graph paper

(you should choose to spread them out across the page)

Label each of the vectors with a name,

(some are named above)

Combine 2 different sets of 2 vectors by drawing them out and finding the resultant

Combine 1 different set of 3 vectors by drawing them out and finding the resultant

Combine 1 set of 4 vectors by drawing them out and finding the resultant

Combine all the vectors and find the resultant

Add the results you got from the different set of vectors, see what you get