Matlab code. Is vector perpendicular to plane? The plane is described by two vec

Question

Matlab code.

Is vector perpendicular to plane? The plane is described by two vectors. Each vectors is A function is needed to determine if a given 3D vector is perpendicular to a plane described by a 2 x 3 matrix [x1,y1,z1; x2, y2, z2] that contains the coordinates of the starting point [xl.y1,z1] and end points [x2, y2, z2] Write a logical function isPerpendicular with three inputs: the two vectors defining the plane and the third vector that needs to be tested for being perpendicular to a plane . Example 1 >>isPerpendicular (a, b, c) ISPerpendicular = logical Example2 >>isPerpendicular (a, b, c ISPerpendicular = logical Example 3 >isPerpendicular(a, b, c) ISPerpendicular = logical

Explanation / Answer

A line is parallel to a plane, if it is perpendicular to the normal vector of the plane. Similarly,
A line is perpendicular to the plane, if it is parallel to the normal vector of the plane.

Hence, if the normal vector of the plane needs to be found:

Code for function isPerpendicular :

function output=isPerpendicular(vector1,vector2,vector3)
iv=cross((vector1(2,:)-vector1(1,:)),(vector2(2,:)-vector2(1,:)));
iline=(vector3(2,:)-vector3(1,:));
if(((iv(1)/iline(1))==(iv(2)/iline(2))) && ((iv(2)/iline(2))==(iv(3)/iline(3))))
output=1;
else if(iv==iline)
output=1;
else
output=0;
end
end
end

NOTE: Save this function file and do not run it, It will be used in the function calling program.

Code for running our function and checking the test data:

clc;clear all;close all;
a=[1 1 0;1 2 3];b=[2 1 3;-1 0 2];c=[3 -8 4;1 1 1];
logical=isPerpendicular(a,b,c);
display(logical);

NOTE: Now run the program, which calls the function saved previously and gives the result.

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