Problem 7 on 6.2

P = {-2,7,3};
Q = {8,-10,4};
R = {6,1,9};

RP = R-P

RQ = R-Q

QP = Q-P

w = QP;
v = RP;

A = 1/2*Sqrt[Norm[w]^2*Norm[v]^2-(w.v)^2]

w = R-Q;
v = P-Q;

A = 1/2*Sqrt[Norm[w]^2*Norm[v]^2-(w.v)^2]

w = P-R;
v = Q-R;

A = 1/2*Sqrt[Norm[w]^2*Norm[v]^2-(w.v)^2]

Let’s find the angle at point P

v = R-P;
w = Q-P;

(Subscript[θ, p])= ArcCos[v.w/(Norm[v]*Norm[w])]

ArcCos[(47/(Sqrt[3315]))]

N[((ArcCos[(47/(Sqrt[3315]))])/°)]

N[VectorAngle[v,w]]

v = P-Q;
w = R-Q;

(Subscript[θ, q])= ArcCos[v.w/(Norm[v]*Norm[w])]

N[((ArcCos[(101/(15 (Sqrt[65])))])/°)]

v = P-R;
w = Q-R;

(Subscript[θ, r])= ArcCos[v.w/(Norm[v]*Norm[w])]

N[((ArcCos[-(13/(5 (Sqrt[51])))])/°)]

N[(Subscript[θ, p])+(Subscript[θ, q])+(Subscript[θ, r])]

f = (E^x);
g = Cos[x];

Integrate[f*g,{x,0,π}]

Integrate[f*f,{x,0,π}]

Integrate[g*g,{x,0,π}]

F = {1,x,x^2,x^3};

For[i=1,i≤ 4,i++,
For[j=1, j≤ 4, j++,
Print[{F[[i]],"*",F[[j]],Integrate[F[[i]]*F[[j]],{x,-1,1}]}]
]
]

G = {1,Cos[x],Cos[2x],Sin[x],Sin[2x]};

For[i=1,i≤ 5,i++,
For[j=1, j≤5, j++,
Print[{G[[i]],"*",G[[j]],Integrate[G[[i]]*G[[j]],{x,0,2π}]}]
]
]