exc 1 theorie

exercise1/Theorie.tex

@@ -120,7 +120,6 @@ $\Rightarrow S \times T \neq T \times S \Rightarrow$ does not commute\\
 \begin{pmatrix}  \sum\limits_{i=1} x_i \\ \sum\limits_{i=1} y_i \\ \sum\limits_{i=1} z_i \end{pmatrix}
 \end{gather*}
 \subsection*{c)}
-
 \begin{align*}
 L(p) &= length(p_x - ((p_x \cdot (\vec{e} + \vec{d} \cdot t)) \cdot \vec{d} \cdot t) - \vec{e}) \\
 Vector &= ( L(p_x), L(p_{x+1}), ... , L(p_{x+n})) \hspace{6em} n \widehat{=} Anz. Punkte \\
@@ -144,9 +143,9 @@ e = \begin{pmatrix} 5 \\ 10 \\ 5 \\\end{pmatrix}= t;
 p = \begin{pmatrix} 0 \\ 0 \\ 0 \\ \end{pmatrix}
 \end{gather*}
 \begin{gather*}
-z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0  \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\
-y_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(y_\phi) & -sin(y_\phi) & 0  \\ sin(y_\phi)&cos(y_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_y\\
-x_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times p_x} \Rightarrow \begin{pmatrix} cos(x_\phi) & -sin(x_\phi) & 0  \\ sin(x_\phi)&cos(x_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_x\\
+z_\phi = \frac {\begin{pmatrix} 0\\0\\1\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(z_\phi) & -sin(z_\phi) & 0  \\ sin(z_\phi)&cos(z_\phi)&0\\ 0&0&1 \\ \end{pmatrix}=R_z\\
+y_\phi = \frac {\begin{pmatrix} 0\\1\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} cos(y_\phi) & 0 & sin(y_\phi)  \\ 0 &1 &0\\ -sin(z_\phi)&0&cos(y_\phi) \\ \end{pmatrix}=R_y\\
+x_\phi = \frac {\begin{pmatrix} 1\\0\\0\\ \end{pmatrix} \times p_x} {1 \times |p_x|} \Rightarrow \begin{pmatrix} 0 & 0 & 0  \\ 0 &cos(x_\phi)&-sin(x_\phi)\\ 0&sin(x_\phi)&cos(x_\phi) \\ \end{pmatrix}=R_x\\
 M = R_x \times R_y \times R_z \\
 \Rightarrow Vector = \begin{pmatrix}
 6.323746006808568\\