[Average Property from a wave function]. The position of a particle in three dimensions is a vector denoted by r=(x,y,z)=xi+yj+xk, where i is a unit vector in the x direction, j is a unit vector in the y direction, and k is a unit vector in the z direction. The three dimensional position operator is given as R^=X^i+Y^j+Z^k, where X^=x is the operator denoting "multiply by x ", Y^=y is the operator denoting "multiply by y ", and Z^=z is the operator denoting "multiply by z ". Show that r=2ai+2bj+2ck for a particle constrained in a three dimensional box with side lengths a,b, and c