Three Dimensional Geometry
Write the equation of the plane whose intercepts on the coordinate axes are 2,−4 and 5 respectively.
A plane passes through a fixed point (a,b,c)˙ The locus of the foot of the perpendicular to it from the origin is a sphere of radius a. 21a2+b2+c2 b. a2+b2+c2 c. a2+b2+c2 d. 21(a2+b2+c2)
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 a plane which passes through the point (1,2,3) and which is equally inclined to the planes x−2y+2z−3=0and8x−4y+z−7=0.
Find the equation of the plane passing through the straight line 2x−1=−3y+2=5z and perpendicular to the plane x−y+z+2=0.
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 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.