Three Dimensional Geometry
Find the distance of the point P(6,5,9) from the plane determined by the points A(3,−1,2), B(5,2,4)and C(−1, −1, 6)˙
Find the equation of the plane that contains the point A(1,−1,2) and is perpendicular to both the planes 2x+3y−2z=5 and x+2y−3z=8. Hence, find the distance of the point P(−2,5,5) from the plane obtained above.
Find the vector and Cartesian equations of the plane passing through the point (3,−1,2) and parallel to the lines r=(−j^+3k^)+λ(2i^−5j^−k^) and r=(i^−3j^+k^)+μ(−5i^+4j^).
Find the equation of the plane passing through the intresection of the planes x−2y+z=1 and 2x+y+z=8 and parallel to the line with direction ratio proportional to 1,2,1, find also the perpendicular distance of (1,1,1) from this plane.