Three Dimensional Geometry
If (a1,b1,c1 and (a2,b2,c2) be the direction ratios of two parallel lines then
A line makes angles, θ,ϕ and ψ with x, y, z axes respectively. Consider the following:1.sin2θ+sin2ϕ=cos2ψ2. cos2θ+cos2ϕ=sin2ψ3.sin2θ+cos2ϕ=cos2ψWhich of the above is/are correct?
Reduce the equation of line x−y+2z=5adn3x+y+z=6 in symmetrical form. Or Find the line of intersection of planes x−y+2z=5and3x+y+z=6.
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.
A variable plane which remains at a constant distance 3p from the origin cut the coordinate axes at A, B and C. The locus of the centroid of triangle ABC 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