Three Dimensional Geometry
A line 4x+3y=24 cut the x-axis at point A and cut the y-axis at point B then incentre of triangle OAB is (A) (4,4) (B) (4,3) (C) (3,4) (D) (2,2)
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If (a1,b1,c1 and (a2,b2,c2) be the direction ratios of two parallel lines then
Show that the line x=(2i^−2j^+3k^)+λ(i^−j^+4k^) is parallel to the plane r⋅(i^+5j^+k^)=7.
Find the angle between the lines r=(2i^−5j^+k^ )+λ(3i^+2j^+6k^ ) and r=(7i^−6k^ )+μ(i^+2j^+2k^ )
Write the equation of the plane whose intercepts on the coordinate axes are 2,−4 and 5 respectively.
The distance between the parallel planes 2x−3y+6z=5 and 6x−9y+18z+20=0, is?
Show that the four points A(3,2,−5),B(−1,4,−3),C(−3,8,−5) and D(−3,2,1) are coplanar. Find the equation of the plane containing them.
Find the equation of the plane passing through the intersection of the planes 4x−y+z=10 and x+y−z=4 and parallel to the line with direction ratios 2,1,1. Find also the perpendicular distance of (1,1,1) from this plane.
If the equations of a line are −33−x=−2y+2=6z+2, find the direction cosines of a line parallel to the given line.