From the point `P(1,2,4)` a perpendicular is drawn on the plane `2x+y-2z+3=0`. Find the equation the length and the coordinates of the foot of perpendicular.

Find the equation of the perpendicular drawn from the point P(-2,3) to the line x-4y+7=0. Also, find the coordinates of the foot of the perpendicular.

Find the foot of the perpendicular drawn from the point (-1, 3, -6) to the plane 2x +y -2z + 5 =0 Also find the equation and length of the perpendicular

Find the length of the perpendicular from the point (2,3,7) to the plane 3 x - y - z = 7 . Also , find the co-ordinates of the foot of the perpendicular .

The foot of the perpendicular drawn from the origin to a plane is (2, -3, -4). Find the equation of the plane.

Find the equation of the perpendicular drawn from the origin to the line 4x-3y+5=0. Also, find the coordinates of the foot of the perpendicular.

Find the equations of the line through (-1,3,2) and perpendicular to the plane x + 2y + 2z = 3, the length of the perpendicular and co-ordinates of its foot.

The foot of the perpendicular drawn from the origin to the plane x+y+z=3 is

(a) Find the length and the foot of the perpendicular from : P (1,1,2) to the plane 2x - 2y + 4z + 5 = 0 (b) Find the co-ordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z - 6 = 0.

The foot of the perpendicular drawn from the origin to a plane is (1,2,-3). Find the equation of the plane.or If O is the origin and the coordinates of P is (1,2,-3), then find the equation of the plane passing through P and perpendicular to OP.

(I) Find the foot and length of the perpendicular from the point (3,4,5) to the plane : 2 x - 5y + 3z = 39 . (ii) Find the length and the foot of the perpendicular from the point (7,14,5) to the plane 2x + 4y - z = 2 .