Trigonometry - Graphing vectors.

[Spellbinder2050]

My book shows three vectors, v, w, and u, which are illustrated geometrically on a plane. Each of them has their own length (magnitude) and direction.

The following operation is performed as an example:

2v + 3w
---------------------------------------------------

Is graphing an accurate depiction of the new magnitude important? If so, I need an explanation of how it is done. My book does not explain how accurate my graph has to be.

Basically, I can figure out the original magnitude of the vector v by using the Pythagorean theorem, but once I multiply it by 2, how do I accurately go about graphing the new magnitude (2v)? Likewise, how would I go about graphing 3w?

Here is a picture of what is in my book, which I've described above:

http://postimage.org/image/uqmaop7bv/

This website is NOT a virus. Just Google postimage.org

[nona.m.nona]

Since you are being asked to graph answers which are based on graphical inputs, yes, you'll need to graph. From the posted example, I would suspect that the text explains the topic fairly succinctly; follow the process illustrated in the example by drawing the first vector at the displayed "angle" (or "slope", if you like) at the specified length (the first example shows v as being X1 in length; the second example shows v as being X2 in length) and direction (the first example shows w going "backwards", since it is negative). From the end of the first vector, draw the second vector. Then draw the third vector starting from the base of the first vector to the tip of the second.

[Spellbinder2050]

I'm not sure where the confusion is with my question. I asked whether the length has to be specific. I never asked anything about the angle or slope.

I'll ask the question again: Does the new vector line 2v have to be measured specifically when graphing it, Or do I kind of just visualize and guess the length of 2v? Likewise, do I measure 3w when graphing it, or do I visualize and guess its length?

Thanks.

[maggiemagnet]

How specific you have to be probably depends on your book and your teacher. If your teacher says to measure, or if your teacher measured when s/he showed examples on the board, then you probably have to use a ruler. You probably should use a ruler anyway!

[jg.allinsymbols]

You must measure the summand vectors, but you can then measure the resulting vector to check your work.

[jg.allinsymbols]

spellbinder2050 asks this:

Is graphing an accurate depiction of the new magnitude important? If so, I need an explanation of how it is done. My book does not explain how accurate my graph has to be.

Yes, graphing a vector, including operations on vectors, is important; at least for the learning process. You want to visualize features of vectors and their components and develop some intuition about vectors. Drawing and graphing are extremely important ways of communicating.