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.2x+3y−z=5.
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What is the equation of the plane through z-axis and parallel to the linex−1cosθ=y+2sinθ=z−30?
Find the equation of a plane containing the line of intersection of the planes x+y+z−6=0and2x+3y+4z+5=0
passing through (1,1,1)
Find the equation of the plane through the points (23,1)and(4,−5,3)
and parallel to the x-axis.
Find the angle between the lines whose direction cosines are connected by the relations l+m+n=0and2lm+2nl−mn=0.
Find the equation of the image of the plane x−2y+2z−3=0
in plane x+y+z−1=0.
Find the ratio in which the y−z
plane divides the join of the points (−2,4,7)and(3,−5,8)˙
Reduce the equation of line x−y+2z=5adn3x+y+z=6
in symmetrical form.
Find the line of intersection of planes x−y+2z=5and3x+y+z=6.
If θ is the acute angle between the diagonals of a cube, then which one of the following is correct?