How do we find out if a given plane contains a given line or not?

Question

Yash Jain · Answer

See, if we have a given line and a given plane, the we know the following things:-
1) the DRs of normal vector of the plane.
2) a fixed point on the line.
3) the DRs of the line.
For a plane to contain a line, it must satisfy two checks.
1) The fixed point must satisfy the equation of the plane.
2) The DRs of the line If the above conditions hold, then we can conclude that the given line is contained in the given plane.
must satisfy the condition of perpendicularity i.e., l1l2 + m1m2 + n1n2 = 0. and that of the normal vector of the plane

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How do we find out if a given plane contains a given line or not?

How do we find out if a given plane contains a given line or not?

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