Three Dimensional Geometry
The projections of a vector on the three coordinate axis are 6,3,2 respectively. The direction cosines of the vector are(A) 6,−3,2 (B) 56,5−3,52 (C) 76,7−3,72 (D) 7−6,7−3,72
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A line makes angles α,β,γandδ
with the diagonals of a cube. Show that cos2α+cos2β+cos2γ+cos2δ=4/3.
Find the angle between the line 3x−1=2y−1=4z−1
and the plane 2x+y−3z+4=0.
Find the locus of a point, the sum of squares of whose distance from the planes x−z=0,x−2y+z=0 and x+y+z=0 is 36
If the lines 2x−1=3y+1=4z−1and1x−3=2y−k=1z
intersect, then find the value of k˙
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)
ABC is a triangle and A=(2,3,5),B=(-1,3,2) and C= (λ,5,μ). If the median through A is equally inclined to the axes, then find the value of λ and μ
If P(x,y,z) is a point on the line segment joining Q(2,2,4)andR(3,5,6) such that the projections of OP on the axes are 13/5, 19/5 and 26/5, respectively, then find the ratio in which P divides QR˙
Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2−y=z+3.