91Ó°ÊÓ

Classify the rigid motions in the plane.

Give an example to show that two non-parallel lines in \(\mathrm{R}^{3}\) need not intersect.

Find a parametric representation of the line passing through \(\mathrm{P}\) and in the direction of u where (a) \(\mathrm{P}=(2,5)\) and \(\mathrm{u}=(-3,4)\); (b) \(\mathrm{P}=(4,-2,3,1)\) and \(\mathrm{u}=(2,5,-7,11)\).