Three Dimensional Geometry
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.
Find the vector equation of a line passing through the point (1,2,3) and parallel to the vector (3i^+2j^−2k^ )
Find the equation of the plane passing through the intersection of the planes 4x−y+z=10 and x+y−z=4 and parallel to the line with direction ratios 2,1,1. Find also the perpendicular distance of (1,1,1) from this plane.
Find the value of λ for which the line 2x−1=3y−1=λz−1 is parallel to the plane r⋅(2i^+3j^+4k^)=4.
Find the equation of the plane which contains two parallel lines given by 1x−3=−4y+2=5z and 1x−4=−4y−3=5z−2.
Find the equation of the plane passing through the origin and perpendicular to each of the planes x+2y−z=1 and 3x−4y+z=5.