%path = "maths/vectors/straight line" %kind = chindnum["problems"] %level = 11 The vector \(\begin{pmatrix}{{chiven.x[0]}}\\{{chiven.x[1]}}\end{pmatrix}\) is orthogonal to the line \({{chiven.x[0]}}x_1{{chutil.sgn(chiven.x[1])}}{{abs(chiven.x[1])}}x_2={{chiven.b}}\). The line can be described with the dot product \(\begin{pmatrix}{{chiven.x[0]}}\\{{chiven.x[1]}}\end{pmatrix}\begin{pmatrix}x_1\\x_2\end{pmatrix} = \begin{pmatrix}{{chiven.x[0]}}\\{{chiven.x[1]}}\end{pmatrix}\begin{pmatrix}v_1\\v_2\end{pmatrix} ={{chiven.b}}\).
\(v_1=0\)
\(v_2=\) %chq()
Sketch \(\begin{pmatrix}{{chiven.x[0]}}\\{{chiven.x[1]}}\end{pmatrix}\left(\begin{pmatrix}x_1\\x_2\end{pmatrix} - \begin{pmatrix}v_1\\v_2\end{pmatrix}\right) ={{chiven.b}}\) für ein \(\vec{x}\not=\vec{v}\).