Three Dimensional Geometry
Find the distance between the parallel planes x+2y−2z+4=0 and x+2y−2z−8=0.
A plane passes through a fixed point (a,b,c)˙ Show that the locus of the foot of the perpendicular to it from the origin is the sphere x2+y2+z2−ax−by−cz=0.
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) .
Find the coordinates of the foot of the perpendicular drawn from point A(1,0,3) to the join of points B(4,7,1)andC(3,5,3)˙
The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is:
The locus of a point, such that the sum of the squares of its distances from the planes x+y+z=0,x−z=0 And x−2y+z=0is 9, is
Find the vector equation of a line passing through 3i^−5j^+7k^ and perpendicular to theplane 3x−4y+5z=8.