How can we show that two planes are parallels ?
Two plane are parallel if:
1. They do not intesect in a line or a point.
For example if we have plane P and plane Q
then P-Q = null set
2. If two planes are parallel, then lines in both planes are parallel.
If L is a line in plane P , T is a line in plane Q,
if L parallel to T, then P is parallel to Q.
An equation of a plane is given by ax+by+cz = d where a,b and c are called direction ratios.
If a1x+b1y+c1z = d1..........(1) and
a2x+b2y+c2z = d2...............(2) are two planes, then the planes are parallel if
a1/a2 = b1/b2= c1/c2 and the constant distance between the two parallel planes is giveven by:
| (d2/sqrt(a2^2+b2^2+c2^2)] - d1/sqrt(a1^2+b1^2+c1^2)|
. The following techniques are used to prove that two planes (P) and (Q) parallels:
- the result of (P) intersecting (Q) is null set , or the result of (P) intersecting (Q) = (P) = (Q).
- (P) and (Q) are parallels both with the same plane
- 2 concurrent lines , parallel with the (Q) plane , belong to the plan (P).
- (P) and (Q) are perpendicular to the same line.