A = {3, 1, 1};
B = {-2, -3, -1};

A . B

Norm[A]

N[A . B/Norm[A]/Norm[B]]

Cross[A, B]

n = {5, -6, 1/2. };
n = n/Norm[n]

Norm[n]

Apa = (A . n)*n

n . Apa/Norm[n]/Norm[Apa]

Ape = Cross[Cross[n, A], n]

Apa + Ape

Apa . Ape

n . Ape/Norm[n]/Norm[Ape]

SetOptions[Plot, TextStyle -> {FontSize -> 18}]

Plot[1 + 2*t, {t, 0, 5}]

Plot[-1 - 4*t, {t, 0, 5}]

SetOptions[ParametricPlot, 
      TextStyle -> {FontSize -> 18}]

ParametricPlot[{1 + 2*t, -1 - 4*t}, {t, 0, 5}]

x[t_] := 1 + 2*t;
y[t_] := -1 - 4*t;

Plot[x[t], {t, 0, 5}]

ParametricPlot[{x[t], y[t]}, {t, 0, 5}]

Dt[x[t], t]

Dt[y[t], t]

vx[t_] := Dt[x[t], t]

vy[t_] := Dt[y[t], t]

Plot[vx[t_], {t, 0, 5}]

Plot[vy[t_], {t, 0, 5}]

ParametricPlot[{vx[t_], vy[t_]}, {t, 0, 5}]