Find a normal vector to the plane `x+2y+3z-6=0`

Find a normal vector to the plane 2x-y+2z=5. Also, find a unit vector normal to the plane.

Find the normal form of the plane x+2y-2z+6=0 . Also find the length of perpendicular from origin to this plane and the d.c.'s of the normal.

Show that the normal vector to the plane 2x+2y+2z=3 is equally inclined with the coordinate axes.

The unit vector normal to the plane x + 2y +3z-6 =0 is (1)/(sqrt(14)) hati + (2)/(sqrt(14))hatj + (3)/(sqrt(14))hatk.

Find the angles at which the normal vector to the plane 4x+8y+z=5 is inclined to the coordinate axes.

Find the vector and cartesian equations of the planes (a) that passes through the point (1,0,-2) and the normal to the plane is (b) that passes through the point (1,4,6) and the normal vector to the plane is the normal vector to the plane is the normal vector to the plane is hat i-2hat j-hat k

Find a unit vector normal to the plane is x-2y+2z=6 .

Find the normal form of the plane 2x+3y-z = 5 . Also find the length of perpendicular from origin and d.c's of the normal to the plane.

Find the equation of the plane which is perpendicular to the plane 5x+3y+6z+8=0 and which contains the line of intersection of the planes x+2y+3z-4=0 and 2x+y-z+5=0

Find the equation of the plane which is perpendicular to the plane 5x+3y+6z+8=0 adn which contains the line of intersection of the planes x+2y+3z-4=0and2x+y-z+5=0