Three Dimensional Geometry
Find the angle between the lines r=(2i^−5j^+k^ )+λ(3i^+2j^+6k^ ) and r=(7i^−6k^ )+μ(i^+2j^+2k^ )
Under which one of the following condition will the two planes x+y+z=7 andαx+βy+γz=3, be parallel (but not coincident)?
A mirror and a source of light are situated at the origin 0 and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction consines of the reflected rays are
If the line x=y=z intersect the line s∈Ax˙+s∈By˙+s∈Cz˙=2d2,s∈2Ax˙+s∈2By˙+s∈2Cz˙=d2, then find the value of 2sinA2sinB˙2sinC˙whereA,B,C are the angles of a triangle.
Find the equation of a sphere which passes through (1,0,0)(0,1,0)and(0,0,1), and has radius as small as possible.
If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.
Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axesI.cos2α+cos2β+cos2γ=−1II. sin2α+sin2β+sin2γ=1Whichoftheaboveiasrecorrect?