Compute the distance between the parallel lines given by

Question

\[\begin{pmatrix} 1 \\ 4 \end{pmatrix} + t \begin{pmatrix} 4 \\ 3 \end{pmatrix}\]
and
\[\begin{pmatrix} -5 \\ 6 \end{pmatrix} + s \begin{pmatrix} 4 \\ 3 \end{pmatrix}.\]

Answer 1

one way: determine where a perpendicular line intersects each, and find the distance between the two points of intersection.

another way: determine the equation of one of the lines, then find the distance to it from a point on the other line, suing the formula

d = |Ax+By+C|/√(A^2+B^2)