3 point problem and Cramers Rule

[succubus]

If anyone in ehre is familiar with the 3-point problem and Cramers Rule, I need some help.

In the evaluation of strike, you are supposed to take the equation for the plane in the horizontal xy plane. But when you arctan the slope, you are supposed to use the slope with x plotted as a functin of y. I don't quite understand this concept. If you need a better explanation you can read about it in this paper written by my teacher.

http://www.nagt.org/files/nagt/jge/columns/CG12-v48n4p522.pdf

Its equation 26.

Any help would be appreciated.

-Pati

 

[Ouabache]

Cramer's Rule is a common mathematical tool for finding the solution of simultaneous equations, by using the ratio of determinants. If you already understand how to solve a 2x2 matrix using determinants, then the following tutorial on Cramer's Rule will be useful. The 3 point problem sounds quite interesting, but is outside the scope of my field. Perhaps some geologists can help here.

 

[Astronuc]

Equation 26 in the cited paper is simply the definition of the strike angle $$\theta_{strike}$$.

Perhaps what is confusing is that the slope of a line in Cartesian coordinates is normally given as dy/dx, and the angle $\theta$ would be arctan (dy/dx) where that angle is the angle between the tangent to y(x) and the horizontal which is parallel to the x-axis.

The complimentary angle (90-$\theta$) would be given by arctan (dx/dy), where x = x(y).

The paper extends this concept to 3D.

Edit: The key to equation 26 is the preceding text: The xy-plane, of course, is horizontal, and so Equation 25 is the equation of a line of strike. The azimuth of strike (θ_strike) is the arctangent of the slope of this line plotted as x vs. y, or:

The key is that in the particular orientation, x vs. y instead of y vs. x, which is the more familiar orientation on conventional 2-D Cartesian (x,y) coordinate systems.