Three Dimensional Geometry
If the lines 1x−2=1y−3=−kx−4 and kx−1=2y−4=1x−5are coplanar, then k can have
Find the vector and Cartesian equations of a plane which is at a distance of 7 units from the origin and whose normal vector from the origin is (3i^+5j^−6k^).
Show that the point (1,2,1) is equidistant from the planes r⋅(i^+2j^−2k^)=5 and r⋅(2i^−2j^+k^)+3=0.
Find the equation of the plane parallel to the plane 2x−3y+5z+7=0 and passing through the point (3,4,−1). Also, find the distance between the two planes.
Write the equations of line parallel to the line −3x−2=2y+3=6z+5 and passing through the point (1,−2,3).
Find the vector equation of the plane passing through the intersection of the planes r⋅(2i^−7j^+4k^)=3 and r⋅(3i^−5j^+4k^)+11=0, and passing through the point (−2,1,3).
Find the coordinates of the point where the line through (3,−4,−5) and (2,−3,1) crosses the plane 2x+y+z=7.