Three Dimensional Geometry
Reduce the equation of the plane 4x−3y+2z to the intercept form, and hence find the intercepts made by the plane with the coordinate axes.
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Under what condition are the two linesy=mℓx+α,z=nℓx+β; and y=m′ℓ′x+α′,z=n′ℓ′x+β′ Orthogonal?
Find the angel between the following pair of lines:
Find the unit vector perpendicular to the plane r2i^+j^+2k^˙=5.
The direction consines of two lines are related byl+m+n=0al2+bm2+cn2=0. The lines are parallel if
The direction ratios of the normal to the plane passing through the points (1, -2, 3), (-1, 2, -1) and parallel to x−22=y+13=z4 is
Find the distance of the point P(a,b,c)
from the x-axis.
Find the distance between the parallel planes x+2y−2z+1=0and2x+4y−4z+5=0.
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.