Kinematics Question 586
Question: The resultant of vectors $ \overrightarrow{\text{P}} $ and $ \overrightarrow{\text{Q}} $ it’s $ \overrightarrow{\text{R}} $ . On reversing the direction of $ \overrightarrow{\text{Q}} $ , the resultant vector becomes $ \overrightarrow{S} $ . Then, correct relation it’s
Options:
A) $ ~R^{2}+S^{2}=(P^{2}+Q^{2}) $
B) $ R^{2}+S^{2}=P^{2}+Q^{2} $
C) $ R^{2}+P^{2}=S^{2}+Q^{2} $
D) $ P^{2}+S^{2}=2(Q^{2}+R^{2}) $
Show Answer
Answer:
Correct Answer: A
Solution:
[a] We have $ R^{2}=P^{2}+Q^{2}+2PQ\cos \theta …(i) $
$ S^{2}=P^{2}+Q^{2}-PQ\cos \theta \text{}…(ii) $
$ \text{Adding equations (i) and (ii) , we get } $
$ R^{2}+S^{2}=2( P^{2}+Q^{2} ). $
