Three Dimensional Geometry
Find the equation of the plane passing through the origin and perpendicular to each of the planes x+2y−z=1 and 3x−4y+z=5.
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What is the equation of the plane through z-axis and parallel to the linex−1cosθ=y+2sinθ=z−30?
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?
If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?
Find the equation of the image of the plane x−2y+2z−3=0
in plane x+y+z−1=0.
The equation of the line which passes through the point (1, 1, 1) and intersect the lines x−12=y−23=z−34 and x+21=y−32=z+14 is
Show that the lines α−δx−a+d=αy−a=α+δz−a−d
The vector a⃗ =αi^+2j^+βk^ lies in the plane of the vectors b⃗ =i^+j^ and c⃗ =j^+k^ and bisects the angle between b⃗ andc⃗ . Then which one of the following gives possible values of a and b?
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.