A sphere of radius 10 units is centred at the origin O(0,0,0). Answer the following:
a. (i) State the formula for the distance of a point P(x,y,z) from the origin.
b. (ii) Without carrying out any numerical calculation, explain how you can decide whether the point P(6,8,2) lies inside the sphere, on its surface, or outside it.
c. (iii) Give a general argument to show that any point satisfying x2+y2+z2<100 lies strictly inside the given sphere.