Obtain the equation of the lines passing through the foot of the perpendicular from (h,k) on the line Ax + By + C = 0 and bisecting the angle between the perpendicular and the given line.

Find the equation of the plane passing through the foot of the perpendiculars drawn from P(a,b,c) on the co-ordinate planes.

Find the length of the perpendicular from (2,0,1) on the line x=y=z .

Write the equation of the line passing through (-3, 1, 2) and perpendicular to the plane 2y - z=3.

Obtain the equation of straight lines : Passing through the points (2,3) and (-4,1) .

Find the equation of lines passing through origin and perpendicular to the lines 3x + 2y - 5 = 0 and 4x + 3y = 7. Obtain the co-ordinate of the points where these perpendiculars meet the given lines . Prove that the equation of line passing through these two points is 23x + 11y - 35 = 0.

Obtain the equation of straight lines : Passing through origin and the points of trisection of the portion of the line 3x + y - 12 = 0 intercepted between the coordinate axes.

Find the equations of the plane passing through the point (2, 1, 3) and perpendicular to the lines (x-1)/1=(y-2)/2=(z-3)/3 .

Find the equation plane passing through the point (2,3,1 )and perpendicular to the line (x-1)/1=(y-2)/-2=(z+1)/3