%% Question 1
% Put your work here

v1 = [0.4082;0.8165;-0.4082];
u1 = [0.5875;0.1073;0.8022];
dotvu = dot(v1,u1)

if dotvu == 0
    q1_result = true
else
    q1_result = false
end

%% Question 2
% Put your work here

v2 = [1;1;1;1;0;0];
u2 = [5;5;5;5;5;5];

q2_result = (dot(v2,u2)*u2)/(norm(u2)^2)

%% Question 3
% Put your work here

v3 = u2;
V1 = v2;
V2 = [1;-1;0;0;1;0];
V3 = [0;-1;1;0;-1;1];
V4 = [0;-1;0;1;-1;-2];
V = [V1 V2 V3 V4];

proj_set = [];
for i = 1:4
    num = dot(v3,V(:,i))*V(:,i);
    proj = num/(norm(V(:,i))^2);
    proj_set = [proj_set, proj];
end

q3_result = proj_set(:,1) + proj_set(:,2) + proj_set(:,3) + proj_set(:,4)

%% Question 4
% Put your work here

% See below \/

%% Question 5a
% Put your work here

p5a = [0 1 0 1];
q5a = [1 0 -1 1];

q5a_result = mypolyinnerproduct(p5a,q5a)

%% Question 5b
% Put your work here

p5b = [1 2 -4];
q5b_result = sqrt(mypolyinnerproduct(p5b,p5b))

%% Question 5c
% Put your work here

p5c = [1 0 0 -5];

q5c_result = p5c/sqrt(mypolyinnerproduct(p5c,p5c))

%% Question 6
% Put your work here

f = [1 -2 0 0];
g = [0 0 1 0];
dotfg = mypolyinnerproduct(f,g);
q6_result = (dotfg*g)/mypolyinnerproduct(g,g)


%% Question 4 Function

function output4 = mypolyinnerproduct(p,q)
P4 = polyint(conv(p,q));
output4 = polyval(P4,1)-polyval(P4,-1);
end