how to analize the graphical method of the vectors?

Answer 1

It's hard to describe without an example.

Answer 2

Vectors have both magnitude and direction. The direction is frequently specified as some angle relative to a coordinate system. For example, in the common X-Y (Cartesean) coordinate system, we might say V = |V| @ theta degrees measured from the X axis. |V| means the magnitude of the vector V.

When analyzing vectors, the first thing you should do is select the best coordinate system. For example, if your vector resides in spherical space, the spherical coordinate system might be the best system to use in analysis because it would be easier to use than, say, an XYZ coordinate system.

Then the next thing, after selecting the best coordinate system, is to reduce the vector V to its component parts along the coordinates of the system you select. For example, in a Cartesean (XY) system, you'd find Vx = |V| cos(theta) and Vy = |V| sin(theta), which are the so-called projections of V onto the X and Y axes respectively.

Now you can do some math. For example, find Z = W + V; where W = |W| @ omega degrees wrt X. We can add the X projections of W and V; so that Zx = Wx + Vx = |W| cos(omega) + |V| cos(theta). Similarly, Zy = |W| sin(omega) + |V| sin(theta).

In which case we can construct the new vector from Z^2 = Zx^2 + Zy^2 because the XY graph is Euclidean space and the sum of the squares of the X and Y sides equals the square of the hypoteneuse, which is |Z| the magnitude of the new vector Z. The direction of Z would then be phi = arctan(Zy/Zx).

And there you have it. To anayze vectors by graph:

First, choose the right graph coordinate system.

Second, break each vector down into its projected components.

Third, do the math on the components.

Finally, construct the answer (e.g., Z) using the results of the math on the components.

Answer 3

http://www.sparknotes.com/physics/vectors/vectoraddition/section2.rhtml
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