Question

How to find if a line is above, below or on the plane, if line and plane are parallel to each other.

Answer 1

even if you dont know any formulae, just randomly pick any 2 points from the line ,find the distance of those 2 points from the place
if distances are equal,then line is parallel to plane

Answer 2

lets try an example:
plane
\[2x-y-z = 3\]
line
\[x(t) = t +A\]
\[y(t) = t+B\]
\[z(t) = t+C\]
if
2A -B-C = 3 , line is on plane

2A-B-C > 3 , line is below plane

2A-B-C < 3 , line is above plane

Answer 3

^ There's no such thing as a line being above/below a plane, a line SEGMENT does, however.

Answer 4

a line can be above or below a plane as long as they are parallel

Answer 5

Given a line (l): x=at+a0, y=bt+b0, z=ct+c0, and a plane (P): mx+ny+pz+q=0, the line can either (i) intersect the plane (ii) parallel to the plane (iii) lie on the plane.
(i) happens iff am+bn+cp does not equal to 0.
Otherwise, pick a point on the line, if it's also on the plane, then the line is on the plane, if not, then the line is parallel to the plane.

Answer 6

did that help?
here is a more general explanation:
plane
\[Ax+By+Cz = D\]
parallel line:
\[x(t) = \frac{2}{A}t + e\]
\[y(t) = -\frac{1}{B}t + f\]
\[z(t) = -\frac{1}{C}t + g\]
line is on plane if:
\[Ae+Bf+Cg = D\]
below plane if:
\[Ae +Bf +Cg > D\]
above plane if:
\[Ae +Bf +Cg < D\]

Answer 7

My bad,even with a line segment there's no such thing as below/above a plane. For example, given the plane x=1 and the line x=y=0, z=t.