Finding the equation of the straight (l1), which passes in point and perpendicular to the straight (l2):
Answer:
There are 2 completely different ways to do this problem:
1. By calculus: Let Q denote a point on
Then calculate the distance which will give you an equation of a function with respect to t. Calculate the minimum distance using the first derivative.
If d(t) has an extreme value then (d(t))^2 has an extreme value too. Therefore it is sufficient if you examine (d(t))^2.
Solve for t.
Calculate the coordinates of Q.
Calculate the equation of the line PQ.
2. By analytic geometry: Calculate the equation of an auxiliar plane a perpendicular to and containing P.
Then calculate the intersection of and a which is the point Q.
Calculate the equation of the line PQ.