Three Dimensional Geometry
Show that the four points A(0,−1,0),B(2,1,−1),C(1,1,1) and D(3,3,0) are coplanar. Find the equation of the plane containing them.
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Find the equation of a line which passes through the point (2,3,4)
and which has equal intercepts on the axes.
A sphere of constant radius k,
passes through the origin and meets the axes at A,BandC˙
Prove that the centroid of triangle ABC
lies on the sphere 9(x2+y2+z2)=4k2˙
A line makes angles α,βandγ
with the coordinate axes. If α+β=900,
then find γ˙
Show that the lines α−δx−a+d=αy−a=α+δz−a−d
Find the vector equation of a line passing through 3i^−5j^+7k^
and perpendicular to theplane 3x−4y+5z=8.
The d. r. of normal to the plane through (1, 0, 0), (0, 1, 0) which makes an angle π/4 with plane x+y=3 are
Find the angel between the following pair of lines:
Find the angle between the lines x−3y−4=0,4y−z+5=0andx+3y−11=0,2y=z+6=0.