Three Dimensional Geometry
Find the equation of the line passing through the point P(4,6,2) and the point of intersection of line 3x−1=2y=7z+1 and the plane x+y−z=8.
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Find the angel between the following pair of lines:
A point P(x,y,z) is such that 3PA=2PB, where AandB are the point (1,3,4)and(1,−2,−1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.
Find the shortest distance between the lines r=(1−λ)i^+(λ−2)j^+(3−2λ)k^andr=(μ+1)i^+(2μ+1)k^˙
The direction consines of two lines are related byl+m+n=0al2+bm2+cn2=0. The lines are parallel if
If a plane meets the equations axes at A,BandC
such that the centroid of the triangle is (1,2,4),
then find the equation of the plane.
Find the angel between the lines 2x=3y=−zand6x=−y=−4z˙
Find the equation of the plane which is parallel to the lines r=i^+j^+λ(2i^+j^+4k^)and−3x+1=2y−3=1z+2
and is passing through the point (0,1,−1
A ray of light passing through the point A(1,2,3)
, strikews the plane xy+z=12atB
and on reflection passes through point C(3,5,9)˙
Find the coordinate so point B˙