%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 \(\vec{x}\not=\vec{v}\).