For any two non-zero vectors A and B, consider the following tasks:
(i) Find the vector component of A along B.
(ii) Obtain the vector component of A perpendicular to B.
(iii) Prove that the two components obtained in parts (i) and (ii) are mutually perpendicular.
(iv) Show algebraically that the vector sum of the components found in parts (i) and (ii) equals the original vector A.