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Grade 11Vectors

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

Profile image of Satviki Pathak
11 Years agoGrade 11
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1 Answer

Profile image of Yash Jain
11 Years ago
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