Three Dimensional Geometry
The direction ratios of normal of a plane passing through two points (0,1,0) & (0,0,1) and makes an angle 4π with the plane y−z−5=0 are (A) (2,−2,2) (B) (2,−1,1) (C) (2,1,1) (D) (2,2,1)
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Find the vector equation of the plane through the point (1,1,1), and passing through the intersection of the planes r⋅(i^−j^+3k^)+1=0 and r⋅(2i^+j^−k^)−5=0.
Find the equation of the plane passing through the points (1,2,3) and (0,−1,0) and parallel to the line 2x−1=3y+2=−3z.
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 acute angle between the following planes.r⋅(i^+j^−2k^)=5 and r⋅(2i^+2j^−k^)=9.
Find the coordinates of the image of the point P(1,3,4) in the plane 2x−y+z+3=0.
Find the angle between the line 2x+1=3y=6z−3 and the plane 10x+2y−11z=3.
From the point P(1,2,4) a perpendicular is drawn on the plane 2x+y−2z+3=0. Find the equation, the length and the coordinates of the foot of the perpendicular.
Find the Cartesian equation of the plane whose vector equation is r⋅(3i^+5j^−9k^)=8.