Three Dimensional Geometry
Find the vector equation of a line passing through the point (1,2,3) and parallel to the vector (3i^+2j^−2k^ )
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Find the radius of the circular section of the sphere ∣r∣=5
by the plane ri^+2j^−k^˙=43˙
Under which one of the following condition will the two planes x+y+z=7 andαx+βy+γz=3, be parallel (but not coincident)?
Which one of the following is the plane containing the lien x−22=y−33=z−45 and parallel to z axis?
The lines which intersect
the skew lines y=mx,z=c;y=−mx,z=−c
and the x-axis lie on the surface:
(d.) none of these
Find the equation of a line which passes through the point (2,3,4)
and which has equal intercepts on the axes.
The Cartesian equation of a line is 2x−3=−2y+1=5z−3
. Find the vector equation of the line.
Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2−y=z+3.
Consider the following relations among the anglesα, β and γ made by a vector with the coordinate axesI.cos2α+cos2β+cos2γ=−1II. sin2α+sin2β+sin2γ=1Whichoftheaboveiasrecorrect?