Three Dimensional Geometry
The distance between the parallel planes 2x−3y+6z=5 and 6x−9y+18z+20=0, is?
Value ofλ such that the linex−12=y−13=z−1λIs perpendicular to normal to the planer⃗ .(2i⃗ +3j⃗ +4k⃗ )=0 is
Determine whether the following pair of lines intersect or not. (1) r=i^−5j^+λ(2i^+k^);r=2i^−j^+μ(i^+j^−k^) (2) r=i^+j^−k^+λ(3i^−j^);r=4i^−k^+μ(2i^+3k^)
A mirror and source of light are situated at the origin O and a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the DRs of the normal to the plane of mirror are 1,−1,1, then DCs for the reflacted ray are :
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0 and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
The extremities of a diameter of a sphere lie on the positive y- and positive z-axes at distance 2 and 4, respectively. Show that the sphere passes through the origin and find the radius of the sphere.
A sphere of constant radius k, passes through the origin and meets the axes at A,BandC˙ Prove that the centroid of triangle ABC lies on the sphere 9(x2+y2+z2)=4k2˙