Three Dimensional Geometry
Find the distance of the point (i^+2j^+5k^) from the plane r⋅(i^+j^+k^)+17=0.
Equation of a line in the plane π=2x−y+z−4=0 which is perpendicular to the line l whose equation is 1x−2=−1y−2=−2z−3 and which passes through the point of intersection of l and π is (A) 1x−2=5y−1=−1z−1 (B) 3x−1=5y−3=−1z−5 (C) 2x+2=−1y+1=1z+1 (D) 2x−2=−1y−1=1z−1
Find the equation of a line which passes through the point (1,1,1) and intersects the lines 2x−1=3y−2=4z−3and1x+2=2y−3=4z+1˙
If the sum of the squares of the distance of a point from the three coordinate axes is 36, then find its distance from the origin.
Find the direction ratios of orthogonal projection of line 1x−1=−2y+1=3z−2 in the plane x−y+2z−3=0. also find the direction ratios of the image of the line in the plane.