The question asks to match List-I with List-II, but the actual contents of List-I items (a), (b), (c), (d) and List-II items (i), (ii), (iii), (iv) are not present in the prompt.

Without those entries, it is impossible to derive the matching logically from physics/vector algebra.

What is missing

To solve a matching question, we need something like:

• List-I: expressions / diagrams / vector identities / physical quantities
• List-II: corresponding results / properties / directions / magnitudes

But only the options are visible:

• A: $(a)\to(iv), (b)\to(i), (c)\to(iii), (d)\to(ii)$
• B: $(a)\to(iv), (b)\to(iii), (c)\to(i), (d)\to(ii)$
• C: $(a)\to(iii), (b)\to(ii), (c)\to(iv), (d)\to(i)$
• D: $(a)\to(i), (b)\to(iv), (c)\to(ii), (d)\to(iii)$

Since the lists themselves are absent, no valid step-by-step physical derivation can be performed.

Conclusion

Based only on the information provided, the answer cannot be independently solved.

However, if I must compare against the stored answer, the stored correct answer is B.

So:

• I cannot verify it from the given data.
• But the stored answer is B.