Three Dimensional Geometry
An equation of a plane parallel to the plane x2y+2z5=0and at a unit distance from the origin is
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Find the length and the foot of perpendicular drawn from the point (2,3,7) to the plane 3x−y−z=7.
Find the acute angle between the following planes.r⋅(2i^−3j^+4k^)=1 and r⋅(−i^+j^)=4.
If the equations of a line are −33−x=−2y+2=6z+2, find the direction cosines of a line parallel to the given line.
Find the distance of the point (0,−3,2) from the plane x+2y−z=1, measure parallel to the line 3x+1=2y+1=3z.
Find the vector and Cartesian equations of a plane which is at a distance of 296 from the origin and whose normal vector from the origin is (2i^−3j^+4k^).
Find the equation of the plane through the line of intersection of the planes r⋅(2i^−3j^+4k^)=1 and r⋅(i^−j^)+4=0 and perpendicular to the plane r⋅(2i^−j^+k^)+8=0.
If a line makes angles α,β and γ with the x-axis, y-axis and z-axis respectively then (sin2α +sin2β +sin2γ )=
What are the direction cosines of the y-axis?