Three Dimensional Geometry
The point of intersection of the line 3x−1=4y+2=−2z−3 and the plane 2x−y+3z−1=0, is
Find the equation of the plane perpendicular to the line 2x−1=−1y−3=2z−4 and passing through the origin.
The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz-plane at the point(0,172,−132). Then
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 a sphere which passes through (1,0,0)(0,1,0)and(0,0,1), and has radius as small as possible.
From a point P(λ,λ,λ), perpendiculars PQ and PR are drawn, respectively, on the lines y=x, z=1 and y=−x, z=−1. If ∠QPR is a right angle, then the possible value(s) of λ is/are