Write a MATLAB code for the following problem: Consider the equation of a plane

Question

Write a MATLAB code for the following problem:

Consider the equation of a plane written as a_1 x+a_2 y+a_3 = z. Given three known points (x_1, y_1, z_1), (x_2, y_2, z_2), and (x_3, y_3, z_3), write the system of equations that determine a_1, a_2, and a_3. Write a plane function that returns the a, given any three points. Test your function by finding the equation of the plane passing through (1, 0, 0), (0, 1, 0), and (0, 0, 1). What are the values of z at (x, y) = (0, 0.5), (0.5, 0), (0.25, 0.25), and (0.5, 0.5)?

Explanation / Answer

plane.m

function a = plane(s1,s2,s3)
A = [s1(1) s1(2) 1;s2(1) s2(2) 1;s3(1) s3(2) 1];
b = [s1(3);s2(3);s3(3)];
a = A;%gives inv(A)*b which is our solution
end

command window log:

>> clear all
>> ai = plane([1 0 0],[0 1 0],[0 0 1])

ai =

-1
-1
1

>> z = (ai(1)*(0))+(ai(2)*(0.5))+ai(3)

z =

0.500000000000000

>> z = (ai(1)*(0.5))+(ai(2)*(0))+ai(3)

z =

0.500000000000000

>> z = (ai(1)*(0.25))+(ai(2)*(0.25))+ai(3)

z =

0.500000000000000

>> z = (ai(1)*(0.5))+(ai(2)*(0.5))+ai(3)

z =

0

>>

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