Ive been stuck on this problem for a while now,
Consider the two lines in the xy-plane, given the equations:
where all four a,b,c and d are nonzero
i) Give the parametric Vector equations for both L1 and L2
ii) Show that L1 and L2 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 L1 and L2 intersect. Find the parametric scalar equations of the line passing through P perpendicular to both L1 and L2.
Now if this didn't have a,b,c and d as variables i thought i would have subbed in points on L1 to give me points to use as r0 in the equation r=r0+tv but im not sure how to tackle it.
any help would be much appreciated.