Three Dimensional Geometry
A plane meets the coordinate axes at A, B and C respectively such that the centroid of ΔABC is (1,−2,3). Find the equation of the plane.
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Find the distance of the point (1,0,−3)
from the plane x−y−z=9
measured parallel to the line 2x−2=2y+2=−6z−6˙
Find the equations of the bisectors of the angles between the planes 2x−y+2z+3=0and3x−2y+6z+8=0
and specify the plane which bisects the acute angle and the plane which bisects the obtuse angle.
Find the image of the point (1,2,3) in the line 3x−6=2y−7=−2z−7.
The foot of the perpendicular from the point (1, 6, 3) to the line x1=y−12=z−23 is
Find the distance of the point (−1,−5,−10)
from the point of intersection of the line 3x−2=4y+1=12z−2
and plane x−y+z=5.
Find the equation of the sphere which has centre at the origin and touches the line 2(x+1)=2−y=z+3.
Find the unit vector perpendicular to the plane r2i^+j^+2k^˙=5.
Find the equation of a plane which is parallel to the plane x−2y+2z=5
and whose distance from thepoint (1,2,3)