Three Dimensional Geometry
The vector equation of a line is r=(2i^+j^−4k^ )+λ(i^−j^−k^ ). find its Cartesian equation.
A line OP through origin O is inclined at 300and450→OXandOY, respectivley. Then find the angle at which it is inclined to OZ˙
If α,β,andγ are the an gles which a directed line makes with the positive directions of the co-ordinates axes, then find the value of sin2α+sin2β+sin2γ˙
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.
If a plane meets the equations axes at A,BandC such that the centroid of the triangle is (1,2,4), then find the equation of the plane.
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