Three Dimensional Geometry
The distance of the point (1, 0, 2) from the point of intersection of the line 3x−2=4y+1=12z−2and the plane x y + z = 16, is :
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Find the vector equation of a plane passing through the point (1,2,3) and parallel to the lines whose direction ratios are 1,−1,−2 and −1,0,2.
Find the acute angle between the following planes.x+y−z=4 and x+2y+z=9.
Find the distance between the planes x+2y+3z+7=0 and 2x+4y+6z+7=0.
The equation of a plane which is perpendicular to (2i^−3j^+k^) and at a distance of 5 units from the origin is?
Show that the line r=(2i^+5j^+7k^)+λ(i^+3j^+4k^) is parallel to the plane r⋅(i^+j^−k^)=7. Also, find the distance between them.
Find the angle between the line 2x+1=3y=6z−3 and the plane 10x+2y−11z=3.
Find the angle between the line r=(2i^−j^+3k^)+λ(3i^−j^+2k^) and the plane r⋅(i^+j^+k^)=3.
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^).