Example: 18  
Find the distance of the point from the plane measured parallel to the line

Solution: 18  
The direction cosines of the line parallel to whom we wish to measure the distance, can be evaluated to be
Thus, any point on the line through with these direction cosines, at a distance from , will have the coordinates
If this point lies on the given plane, we have
Thus, the required distance is unit.

Example: 19  
Find a set of direction ratios of the line

Solution: 19  
The equation of the line has been specified in unsymmetric form, i.e., as the intersection of two nonparallel planes.
Visualise in your mind that when two planes intersect, the line of intersection will be perpendicular to normals to both the planes. Normal vectors to the two planes can be taken to be
Thus, the line of intersection will be parallel to i.e. to
A set of direction ratios of the line of intersection can be taken to be

Example: 20  
Find the equation of the plane passing through the line
and parallel to the line

Solution: 20  
In terms of a parameter the equation of the plane that we require can be written as
For this plane to be parallel to the given line, its normal must be perpendicular to the given line. Using the condition for perpendicularity, we thus have
Using this value of in we get the required equation of the plane as
