Zum Inhalt springen

Lösung Ortogonalität prüfen

Version 3.1 von Daniel Stocker am 2024/02/05 11:47

a) cos(\alpha) = \frac{\vec a \cdot \vec b}{\mid\vec a \mid \cdot \mid \vec b \mid} = \frac{7\cdot (-1)+5\cdot 2 + (-3) \cdot (-2) }{\sqrt{7^2+5^2+(-3)^2}\cdot \sqrt{(-1)^2+2^2+(-2)^2}} = \frac{9}{\sqrt{83} \cdot 3} = \frac{3}{\sqrt{83}}
\Rightarrow \alpha \approx 70,77°
b) cos(\alpha) = \frac{\vec a \cdot \vec c}{\mid\vec a \mid \cdot \mid \vec c \mid} = \frac{7\cdot 1,5+5\cdot 2,1 + (-3) \cdot 7 }{\mid\vec a \mid \cdot \mid \vec c \mid} = \frac{0}{\mid\vec a \mid \cdot \mid \vec c \mid} = 0
\Rightarrow \alpha = 90°