posted by Gabe .
Determine the caresian equaiton of a plane that pass through point P(1,2,2) and is perpendicular to the line (x,y,z)= 3,-1,-4 + t(-2,3,1)
If the plane is perpendicular to
in which the vector (-2,3,1) is parallel to the line, and therefore perpendicular to the plane P, then
the required plane is:
where k is a constant to be determined.
Since the required plan passes through P(1,2,2), we substitute P in the plane to get:
Therefore the plane is given by:
Check by joining any two distinct points on the plane to form a vector and prove that the vector is perpendicular to line L.