Three Dimensional Geometry
Find the angle between any two diagonals of a cube.
The equation of the line which passes through the point (1, 1, 1) and intersect the lines x−12=y−23=z−34 and x+21=y−32=z+14 is
A horizontal plane 4x−3y+7z=0 is given. Find a line of greatest slope passes through the point (2,1,1) in the plane 2x+y−5z=0.
If the straight lines x=−1+s,y=3−λs,z=1+λsandx=2t,y=1+t,z=2−t, with paramerters sandt, respectivley, are coplanar, then find λ˙
The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.