Three Dimensional Geometry
Find the acute angle between the following planes.
x+2y+2z=3 and 2x−3y+6z=8.
Find the equation of the plane which passes through the point (1,2,3) and which is at the minimum distance from the point (−1,0,2)˙
The equation of the plane through the intersection of the planes x+2y+3z−4=0and4x+3y+2z+1=0 and passing through the origin is (a) 17x+14y+11z=0 (b) 7x+4y+z=0 (c) x+14+11z=0 (d) 17x+y+z=0
Find the shortest distance between lines r=(i^+2j^+k^)+λ(2i^+j^+2k^)andr=2i^−j^−k^+μ(2i^+j^+2k^)˙
The pair of lines whose direction cosines are given by the equations 3l+m+5n=0and6mn−2nl+5lm=0 are a. parallel b. perpendicular c. inclined at cos−1(61) d. none of these