Originally Posted by

**olliethechum** Ive been stuck on this problem for a while now,

Consider the two lines in the xy-plane, given the equations:

L_{1}:ax+by=k

L_{2}:cx+dy=l

where all four a,b,c and d are nonzero

i) Give the parametric Vector equations for both L_{1 }and L_{2}

ii) Show that L_{1} and L_{2} intersect in a single point if and only if ad-bc≠0

iii) Suppose that ad-bc≠0, and let P be the point where L_{1} and L_{2} intersect. Find the parametric scalar equations of the line passing through P perpendicular to both L_{1} and L_{2}.

Now if this didn't have a,b,c and d as variables i thought i would have subbed in points on L_{1} to give me points to use as r_{0} in the equation r=r_{0}+tv but im not sure how to tackle it.

any help would be much appreciated.