Why we draw rectangular compnents of a vector?

[Aladin]

Please explain me:what is the main purpose to drawing the rectangular components of a vector and why we draw them
thanks.

 

[Dr.Brain]

Example of where we need vectors is for describing motion in more than one dimension.Horizontal and Vertical are the two main directions we look for when trying to simplify problems and for general analysis.Generally vectorial quantities will be in directions making tedious angles with horizontal and vertical, so we take components of these vectors in two prependicular directions.The direction vector and velocity vector of a projectile motion will be a good practice and will tell you the importance of vectors.

BJ

 

[SGT]

The retangular coordinates of a vector are scalar numbers. So, if you have a set of vectors and represent each of them by its retangular coordinates, you can sum the scalars in each axis and find the coordinates of the resultant.

 

[dextercioby]

Because the cosine theorem is simplest when the triangle is rectangular.We then have the celebrated Pythagora's theorem to play with.

And because we invented the Gram-Schmidt orthogonalization procedure.

Daniel.

 

[shyboy]

Not necessarily. Sometimes it is usefull to use polar coordinates. In many cases equations looks easier for the ortogonal Decart system, but sometimes they are not.
Or, one may say, it is because the empty space-time is flat.

 

[Aladin]

sorry I could not understant.please explain with a example.
thank you.

 

[arildno]

And because we invented the Gram-Schmidt orthogonalization procedure.

Daniel.

Disclaimer:
I did not invent the procedure; Gram and Schmidt did.

 

[shyboy]

An example:
if we want to find out how a electromagnetic wave propagates in a rectangular waveguide, we will use Cartesian (Decart) coordinates. If we want to solve the problem for cylindrical waveguide. we will use cylindrical coordinates. For sphericaly symmetric cases one may find that it is better to use spheical coordinates, where vectror is tedermined by its magnitude and two angles.
The main idea of this manipulations is to separate different inputs. We know, for example, that a gravition force depend only on distance between two points and is along the line which connects them. Thus we can expect that equations of motion may look simpler if we choose one coordinate as the distance between two points.

 

[Gokul43201]

Please explain me:what is the main purpose to drawing the rectangular components of a vector and why we draw them
thanks.

The purpose is to be able to rewrite a vector equation in terms of a set of scalar equations so as to be able to solve for the components of the required vectors.

Remember, a vector has as many components as the space it lives in, so to completely specify a vector in n dimensions, you must specify n (linearly) independent things about it.