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

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

Reduce the equation of the plane x-2y-2z=12 to normal form and hence find the length of the perpendicular for the origin to the plane. Also, find the direction cosines of the normal to the plane.

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

Reduce the equation 2x-3y-6z=14 to the normal form and hence fine the length of perpendicular from the origin to the plane. Also, find the direction cosines of the normal to the plane.

If veca,vecbandvecc determine the vertices of a triangle, show that (1)/(2)[vecbxxvecc+veccxxveca+vecaxxvecb] givens the vector area of the triangle. Hence, deduce the condition that the three points veca,vecband vecc are collinera. Also, find the unit vector normal to the plane of the triangle.

Find the equation of the plane which passes through the point (3,4,-1) and is parallel to the plane 2x-3y+5z+7=0. Also, find the distance between the two planes.

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.

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

Find the intercepts made on the coordinate axes by the plane 2x+y-2z=3 and find also the direction cosines of the 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.