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Mathematik-Online problems:

Problem 16: Perpendicular Lines, Orthonormal Basis

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
Let $ O=(0, 0, 0)$ , $ P_1=(1, 2, 2)$ and $ P_2=(2, 1, -2)$ be points in $ \mathbb{R}^3$ and let $ g_1$ be the line through $ O$ and $ P_1$ and $ g_2$ the line through $ O$ and $ P_2$ .
a)
Show that $ g_1$ and $ g_2$ are orthogonal.
b)
Give a parameter representation of $ g_3$ , the line that intersects $ g_1$ and $ g_2$ in the point $ O$ orthogonal.
c)
Find a orthonormal right-handed coordinate system $ \{\vec{b_1},\vec{b_2}, \vec{b_3}\}$ , so that each $ \vec{b_i}$ has the direction of the line $ g_i$ ($ i=1, 2, 3$ ).

(Authors: Kimmerle/Roggenkamp/Höfert)

see also:

[Solutions]
  automatisch erstellt am 9.  5. 2008