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

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

Find the foot of perpendicular drawn from origin to the plane 2x+3y+4z-12=0

Find the equation of the plane passing through the point (3,-3, 1) and perpendicular to the line joining the points (3, 4, - 1) and (2, - 1,5). Also find the coordinates of the foot of the perpendicular, the equation of the perpendicular line and the length of perpendicular drawn from the origin to the plane.

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

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

The foot of perpendicular drawn from the origin to a plane is (2,5,7). Find the vector equations of the plane.

Find the perpendicular distance of the point (1,0,0) from the line : (x-1)/2=(y+1)/-3=(z+10)/8 . Also find the co ordinates 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-ordeinates of its foot.

Find the equation of the perpendicular drawn from the point P(2,4,-1) to the line : (x+5)/1=(y+3)/4=(z-6)/-9 . Also write down the co ordinates of the foot of the perpendicualr from P to the line.

The length of the perpendicular drawn from the origin to 2x-3y+6z+21=0