Three Dimensional Geometry
Find the angle between the planes r⋅(3i^−4j^+5k^)=0 and r⋅(2i^−j^−2k^)=7.
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Find the equation of line x+y−z−3=0=2x+3y+z+4
in symmetric form. Find the direction of the line.
A line makes the same angle α with each of the x and y axes. If the angleθ, which it makes with the z-axis, is such thatsin2θ=2sin2α, then what is the value ofα?
Under what condition are the two linesy=mℓx+α,z=nℓx+β; and y=m′ℓ′x+α′,z=n′ℓ′x+β′ Orthogonal?
The equation of the plane which makes with co-ordinate axes, a triangle with its centroid (α,β,γ)is
If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?
The foot of the perpendicular from the point (1, 6, 3) to the line x1=y−12=z−23 is
Find the equation of the sphere passing through (0,0,0),(1,0,0),(−,1,0)and(0,0,1)˙
Find the direction ratios of orthogonal projection of line 1x−1=−2y+1=3z−2 in the plane x−y+2z−3=0. also find the direction ratios of the image of the line in the plane.