Three Dimensional Geometry
Equation of the plane containing the straight line 2x=3y=4z and perpendicular to the plane containing the straight lines 2x=4y=2z and 4x=2y=3z is
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Find the distance of the point (2,1,−1) from the plane x−2y+4z=9.
Find the vector and Cartesian equations of a plane which is at a distance of 5 units from the origin and which has 3i^−2j^+6k^ as the unit vector normal to it.
What are the direction cosines of the vector (2i^+j^−2k^ )?
Write the equation of the plane passing through the origin and parallel to the plane 5x−3y+7z+11=0.
Find the angle between planes 2x+y−2z=5 and 3x−6y−2z=7
Find the equation of the plane passing through the intresection of the planes x−2y+z=1 and 2x+y+z=8 and parallel to the line with direction ratio proportional to 1,2,1, find also the perpendicular distance of (1,1,1) from this plane.
Find the point where the line 2x−1=−3y−2+4z+3 meets the plane 2x+4y−z=1.
Find the value of m for which the line r=(i^+2k^)+λ(2i^−mj^−3k^) is parallel to the plane r⋅(mi^+3j^+k^)=4.