A point D(1,y,z) lies on the plane x+y+z=6 and is 7 units away from the point E(4,−2,1).
a. (i) Form the two simultaneous equations that arise from the given conditions.
b. (ii) Solve the simultaneous equations to obtain all possible coordinates of D.
c. (iii) Show that every coordinate found indeed satisfies both the plane and distance conditions.