Al Azhar university Lama El Banna general physic

1. > restart:
> with(LinearAlgebra):assume(b, real);
> A:=<-6,b,2>;
:=A
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-6
b~
2
> B:=<b,b^2,b>;
:=B
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b~
b~2
b~
> eq1:=DotProduct(A,B);
:=eq1 − +4 b~ b~3
> solve(eq1=0,b);
, ,0 2 -2
> A1:=<3,-1,3>;
:=A1
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3
-1
3
> B1:=<1,1,-1>;
:=B1
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1
1
-1
> VectorAngle(A1,B1);
−π
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arccos
19 3
57
> evalf(%);
1.703639943
> convert(%,degrees);
306.6551897 degrees
π
> evalf(%);
97.61137851 degrees
> A2:=<1,-2,3>;
:=A2
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> B2:=<1,-1,2>;
:=B2
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> VectorAngle(A2,B2);
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3 14 6
28

2. > evalf(convert(%,degrees));
10.89339472 degrees
> A3:=<-1,2,0>;
:=A3
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2
0
> B3:=<1,0,-2>;
:=B3
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0
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> C3:=<0,-2,2>;
:=C3
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2
> D3:=Add(A3,B3);
:=D3
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2
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> T3:=Add(A3,-C3);
:=T3
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4
-2
> VectorAngle(D3,T3);
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2 21
7
> evalf(convert(%,degrees));
22.20765430 degrees
> E3:=CrossProduct(A3,C3);
:=E3
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> F3:=CrossProduct(B3,C3);
:=F3
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> Norm(E3,2);
2 6
> Eh:=E3/%;

3. :=Eh
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6
3
6
6
6
6
> thickness:=Volume/Area;
:=thickness
Volume
Area
> Area:=25.0;
:=Area 25.0
> Volume:=3.78*10^(-3);
:=Volume 0.003780000000
> thickness;
0.0001512000000
>