Three Dimensional Geometry
Find the vector equation of a plane whose Cartesian equation is 5x−7y+2z+4=0.
Find the vector equation of the following planes in Cartesian form: r=i^−j^+λ(i^+j^+k^)+μ(i^−2j^+3k^)˙
Find the equation of the sphere described on the joint of points AandB having position vectors 2i^+6j^−7k^and−2i^+4j^−3k^, respectively, as the diameter. Find the center and the radius of the sphere.
If Q is the image of the point P(2, 3, 4) under the reflection in the plane x−2y+5z=6, then the equation of the line PQis