Wenn der Vektor um 30% kürzer sein soll, hat er noch 70% seiner Länge:

${\vec{v}}_{neu}=\mathrm{0,7}\cdot \vec{v}=\mathrm{0,7}\cdot \left(\begin{array}{c}120\\ 30\\ -75\end{array}\right)=\left(\begin{array}{c}84\\ 21\\ -\mathrm{52,5}\end{array}\right)\backslash vec\; v\_\{neu\}=0\{,\}7\backslash cdot\backslash vec\; v=0\{,\}7\backslash cdot\; \backslash begin\{pmatrix\}120\backslash \backslash 30\backslash \backslash -75\backslash end\{pmatrix\}=\backslash begin\{pmatrix\}84\backslash \backslash 21\backslash \backslash -52\{,\}5\backslash end\{pmatrix\}$