In: Advanced Math

1. Magnitude & Direction of Vector

Write a function m-file to find the magnitude and the direction of cosine of vector F which expresses 3 dimension - x, y, and z.

Here are requirements for the function m-file.

- Parameter-list (input(s)): · 3 dimensional vector · row vector or column vector

- undetermined - Return Value (outputs):

· Magnitude of a given vector, |F| = √ F2 x + F2 y + F2 z

· Angles(degree) from direction of cosine cos(α) = Fx |F| cos(β) = Fy |F| cos(γ) = Fz |F|

· Order of outputs : [Magnitude, α, β, γ]

- Function name : ‘Mag_Vec_yourEmailAccount’ Using a script m-file which will call the Mag_Vec_yourEmailAccount function, save outputs with following given inputs. - F1 = 3ˆi + 2ˆj − 6ˆk. Save it on EX1_1.dat.

- F2 = 4ˆi − 2ˆk. Save it on EX1_2.dat.

- F3 = 4ˆi + 3ˆj. Save it on EX1_3.dat.

- F4 = 5ˆj − 12ˆk. Save it on EX1_4.dat.

- F5 =ˆi +ˆj + ˆk. Save it on EX1_5.dat.

using mathlab functions, thank you!

function [Magnitude, alp, bit, gamma] = Mag_Vec(F)

Magnitude=sqrt(F(1)^2+F(2)^2+F(3)^2);

alp = acos(F(1)/Magnitude); % acos = invers cos(th)

bit = acos(F(2)/Magnitude); % alp, bit ,gamma calculating as
radian

gamma = acos(F(3)/Magnitude);

alp = 180*alp/pi; % alp, bit ,gamma calculating as degree

bit = 180*bit/pi;

gamma = 180*gamma/pi;

end

clc

clear

fid = fopen('EX1_1.dat','w');

F1=[3, 2, -6]; % F1 = 3i+2j-6k;

[Magnitude, alp, bit, gamma] = Mag_Vec(F1);

Sol = [Magnitude, alp, bit, gamma];

fprintf(fid,'%f \n',Sol);

fclose(fid);

fid = fopen('EX1_2.dat','w');

F2=[4, 0, -2]; % F1 = 4i-2k;

[Magnitude, alp, bit, gamma] = Mag_Vec(F2);

Sol = [Magnitude, alp, bit, gamma];

fprintf(fid,'%f \n',Sol);

fclose(fid);

fid = fopen('EX1_3.dat','w');

F3=[4, 3, 0]; % F1 = 4i+3j;

[Magnitude, alp, bit, gamma] = Mag_Vec(F3);

Sol = [Magnitude, alp, bit, gamma];

fprintf(fid,'%f \n',Sol);

fclose(fid);

fid = fopen('EX1_4.dat','w');

F4=[0, 5, -12]; % F1 = 4j+12k;

[Magnitude, alp, bit, gamma] = Mag_Vec(F4);

Sol = [Magnitude, alp, bit, gamma];

fprintf(fid,'%f \n',Sol);

fclose(fid);

fid = fopen('EX1_5.dat','w');

F5=[1, 1, 1]; % F1 = i+j+k;

[Magnitude, alp, bit, gamma] = Mag_Vec(F5);

Sol = [Magnitude, alp, bit, gamma];

fprintf(fid,'%f \n',Sol);

fclose(fid);

%to see the EX1_1.dat file enter in command window- type EX1_1.dat

The vector A has a magnitude of 16.5 and a direction of 146
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degrees. All angles are measured counterclockwise from the positive
x axis. The vector D follows the following relation: D = A + B − C
What are the magnitude and direction of the vector D?

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Get the distance between two positions.
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Get a point on a ray (given the origin,
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Part B
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|A⃗ | =
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1.Find the derivative of the product between a scalar function
and a vector function using the product formula.
2. Find the volume of an irregular solid using triple
integration, the first integral should have at least one limit with
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limit with variables.
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