Three Dimensional Geometry
Find the angle between the line r=(3i^+k^)+λ(j^+k^) and the plane r⋅(2i^−j^+2k^)=1.
Find the equation of a plane containing the line of intersection of the planes x+y+z−6=0and2x+3y+4z+5=0 passing through (1,1,1) .
If the plane 2ax−3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8 then a equals
Find the radius of the circular section in which the sphere ∣r∣=5 is cut by the plane ri^+j^+k^˙=33.
A line passes through the points (6,−7,−1)and(2,−3,1)˙ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.