matrix Consider the points A : (5,-3,2), B : (2,1,0), C : (-3,2,8) and the vecto

Question

matrix

Consider the points A : (5,-3,2), B : (2,1,0), C : (-3,2,8) and the vector n = (1,1,1) Find the vector equation of the plane through the points A, B and C. Find the standard equation of the plane that goes through A and has normal n = (1, 1, 1). Are these planes perpendicular, parallel or neither? Research a method to find the line of intersect of two planes. Use this method to find the intersect of the planes from (a) and (b). Often we have a set of data from an experiment and we want to fit a straight line (or other curve) to that data. A common approach to this is to use the method of least squares to find the line of best fit. This approach involves solving a linear system called the normal equation. A experiment was conducted with the following results We would like to determine if x and y have a linear or quadratic relationship. Research using the method of least squares to find the line of best fit to find an expression for the normal equation. Use the normal equation to fit a straight line to the data. Use the normal equation to fit a parabola to the data. Graph the data using appropriate software and your fitted curves on the same axis. Which do you think fits the data best? Construct or research a mathematical method to determine which line fits best. Describe the method and use it to determine which of the curves gives the best fit.

Explanation / Answer

I don't know whole. But trying as much as I can

2(c) These planes are nither parralel nor perpendicular.

2(d) Just take cross product of normals and get one point on the line by solving both the equations of planes.

So in this case

(2,2,1)X(1,1,1) = (1,-1,0)

and and get one point common in 2x+2y+z-6=0 and x+y+z-4=0 so lets just take y=0 so x=2 and z=2

so line is 1*(x-2) = -1*(y) = 0(z) = 0

x - x1 y - y1 z - z1 = 0 x2 - x1 y2 - y1 z2 - z1 x3 - x1 y3 - y1 z3 - z1

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