Three Dimensional Geometry
Find the angle between the lines whose direction ratios are:
1,1,2 and (3−1),(−3−1),4
Find the equation of a plane passing through the point (2,−1,5), perpendicular to the plane x+2y−3z=7 and parallel to the line 3x+5=−1y+1=1z−2.
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.
Find the equation of the plane through the line of intersection of the planes r⋅(2i^−3j^+4k^)=1 and r⋅(i^−j^)+4=0 and perpendicular to the plane r⋅(2i^−j^+k^)+8=0.
Find the vector and Cartesian forms of the equations of the plane containing the two lines r=(i^+2j^−4k^)+λ(2i^+3j^+6k^) and r=(3i^+3j^−5k^)+μ(−2i^+3j^+8k^).