Three Dimensional Geometry
For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.3y+5=0.
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Find the vector equation of the line passing through (1,2,3)
and parallel to the planes ri^−j^+2k^˙andr3i^+j^+k^˙=6.
Find the image of the line 9x−1=−1y−2=−3z+3 in the plane 3x−3y+10z−26=0.
Find the equation of the plane passing through A(2,2,−1),B(3,4,
Also find a unit vector perpendicular to this plane.
Find the angle between the line r=i^+2j^−k^+λ(i^−j^+k^)
and the plane r2i^−j^+k^˙=4.
Under what condition does the equation x2+y2+z2+2uc+2uy+2wz+d=0 represent a real sphere?
Show that ax+by+r=0,by+cz+p=0andcz+ax+q=0
are perpendicular to x−y,y−zandz−x
Find the direction ratios of orthogonal projection of line 1x−1=−2y+1=3z−2 in the plane x−y+2z−3=0. also find the direction ratios of the image of the line in the plane.
What is the angle between the planes2x−y+z=6 andx+y+2z=3?