Three Dimensional Geometry
Find the point where the line 2x−1=−3y−2+4z+3 meets the plane 2x+4y−z=1.
The foot of the perpendicular drawn from the origin to a plane is (1,2,−3)˙ Find the equation of the plane. or If O is the origin and the coordinates of P is (1,2,−3), then find the equation of the plane passing through P and perpendicular to OP˙
A plane passing through (1, 1, 1) cuts positive direction of coordinate axes at A, B and C, then the volume of tetrahedron OABC satisfies
A point P(x,y,z) is such that 3PA=2PB, where AandB are the point (1,3,4)and(1,−2,−1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.
Find the length and the foot of the perpendicular from the point (7, 14, 5) to the plane 2x+4y−z=2. Also, the find image of the point P in the plane.
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.