Three Dimensional Geometry
The distance of the point (1,−5,9)from the plane x−y+z=5measured along the line x=y=zis :
Find the equation of the plane passing through the points A(−1,1,1) and B(1,−1,1) and perpendicular to the plane x+2y+2z=5.
If O be the origin and P(1,2,−3) be a given point, then find the equation of the plane passing through P and perpendicular to OP.
The equations of a line are 24−x=2y+3=1z+2. Find the direction cosines of a line parallel to this line.
Find the vector equation of a line passing through the point (2i^−3j^−5k^) and perpendicular to the plane r⋅(6i^−3j^+5k^)+2=0.
Also, find the point of intersection of this line and the plane.
If a line makes angles α,β and γ with the x-axis, y-axis and z-axis respectively then (sin2α +sin2β +sin2γ )=
Find the vector and cartesian equations of the plane passing through the point (2,−1,1) and perpendicular to the line having direction ratios 4,2,−3.
Find the equation of the plane passing through the point A(−1,−1,2) and perpendicular to each of the planes 3x+2y−3z=1 and 5x−4y+z=5.