SOLUTION: Determine the equation of the line that passes through the point A(1,0,2) and intersects the line r=(-2,3,4)+s(1,1,2) at a right angle.

Algebra ->  Vectors -> SOLUTION: Determine the equation of the line that passes through the point A(1,0,2) and intersects the line r=(-2,3,4)+s(1,1,2) at a right angle.      Log On


   

Question 462787: Determine the equation of the line that passes through the point A(1,0,2) and intersects the line r=(-2,3,4)+s(1,1,2) at a right angle.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
The given line r=(-2,3,4)+s(1,1,2) is symmetric form
%28x%2B2%29%2F1+=+%28y-3%29%2F1+=+%28z+-+4%29%2F2. The direction vector is thus given by <1,1,2>. A direction vector of the line perpendicular to this is <1,1,-1>. The symmetric equation of the perpendicular equation is thus
%28x-1%29%2F1+=+y%2F1+=+%28z+-+2%29%2F-1, or R = (1,0,2) + t(1,1,-1).