(a) The equation of the plane is z = 2 or 0x + 0y + z = 2 … (1) The direction ratios of normal are 0, 0, and 1.
This is of the form lx + my + nz = d, where l, m, n are the direction cosines of normal to the plane and d is the distance of the perpendicular drawn from the origin. Therefore, the direction cosines are 0, 0, and 1 and the distance of the plane from the origin is 2 units.
(b) x + y + z = 1 … (1) The direction ratios of normal are 1, 1, and 1.
This equation is of the form lx + my + nz = d, where l, m, n are the direction cosines of normal to the plane and d is the distance of normal from the origin.
(c) 2x + 3y − z = 5 … (1) The direction ratios of normal are 2, 3, and −1.
This equation is of the form lx + my + nz = d, where l, m, n are the direction cosines of normal to the plane and d is the distance of normal from the origin.
This equation is of the form lx + my + nz = d, where l, m, n are the direction cosines of normal to the plane and d is the distance of normal from the origin. Therefore, the direction cosines of the normal to the plane are 0, −1, and 0 and the distance of normal from the origin is 8/5 units.
