Where Can I Learn the Basics of Euclidean Geometry and Vector Calculations?

[RufusDawes]

Does anyone know of a site that will help me learn mathematics ?.

Having trouble with Euclidean geometry and vectors. Need a good source to read up on it and some examples would be good too.

 

[mace2]

If you have a library nearby I would reocmmend trying to find a text there... not sure what to suggest, but maybe have a flip through until you find something suitable?

 

[symbolipoint]

How is your Algebra knowledge? Have you previously studied Euclidean Geometry (assuming you mean "College Preparatory...") before?

Certain people do poorly in Euclidean Geometry during their first year studying but do better in their other three years of Math in high school. After all of that development, ... Geometry becomes easier to learn when studied a second time. What do you find to be difficult about Geometry and Vectors right now?

 

[RufusDawes]

I am having trouble understanding how to find the cartesian equation.

I can do it it mechanically but I do not understand how it works, at all.

I'm not in high school I am going over a first year University mathematics course to try to learn it all before I consider going back to college as it has been a while ( 6 years ) since I have really done any pure math.

Find the vector equation of the plane containing the points (1,2,7),(2,3,4) and (-1,2,1)

 

[Vid]

Form two vectors from your 3 points.
V1 = P2 - P1
V2 = P3 - P1

We can then use these two vectors to find a vector N perpendicular to the plane.
N = V1XV2 , where X is the cross product.

Now we realize that a vector r is in the plane iff the dot product (r-P1).N = 0. (ie: If the vector from P1 to r is orthogonal to n, then r is on the plane.)

r is simply an arbitrary position vector given by (x,y,z).
P1 is a given point (x_o, y_o, z_o)
n is V1 X V2 = (A, B, C)
The equation then becomes
(x-x_o, y-y_o, z-z_o).(A,B,C) = 0
A( x - x_o) + B(y - y_o) + C(z - z_o) = 0

Most calculus texts have a whole chapter or two on vectors and vector geometry so I suggest reading that first.