ONE MORE STEP TOWARD BETTER TOMMOROW
Saturday, 9 August 2014
CHAPTER 7 - Worked Out Examples 2
Find the angle of intersection of the two planes
From the equations of the planes, it is evident that the following vectors are to these planes arespectively:
Since the acute angle
between the two planes will be the acute angle between their normals, we have
Incidentally, we can now derive the conditions for these planes to be parallel or perpendicular.
Planes are parallel if
Plames are perpendicular if
It should be obvious that for two parallel planes, their equations can be written so that they differ only in the constant term. Thus, any plane parallel to
can be written as
Find the distance of the point
from the plane
Find the distance beween the two parallel lines
from the given plane will obviously be measured along the normal to the plane passing through
We write the equation of the plane as
is any point on the plane and
is the normal to the plane.
be the origin. Since
lies on the plane, its position vector
must satisfy the equation of the plane. But
(which sign to take depends on which direction
Assume any point
on the first plane. We have
The distance of
from the second plane, say
, can be evaluated as described in part
This is the required distance between the two planes
August 09, 2014
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