If a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2.

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ashuhra6e · Accepted Answer

Step 1  From Geometry: Line can be parallel to plane, intersect the plane or lie in the plane. Only third case allows the fact that two points of the lines are also the points of plane.   Step 2 From analytical geometry: Line parametric equation is P=P1=(P1−P2)t.  Plane equationn(U−P1)=0  Where n is normal vector U is arbitory point of plane . ifP2 is in plane than  n(P2−P1)+0  n(P−P1)=tn(P2−P1)=0  Therefore any line point lies on the plane

chicasdelperuszp · Accepted Answer

Step 1  Given query is to prove If a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2.  Step 2  Since we know that a plane is nothing but a surface (flat) , if we make a line connecting two distinct points on this surface the resulting line will be on this plane itself.  Moving further a line is a connection of several points since this line is on the surface the points on the line will also lie on this plane.  If we combine both above statment, that will prove that If a plane contains two distinct points P1 and P2 then show that it contains every point on the line through P1 and P2.

If a plane contains two distinct points P1 and P2

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