Vector Algebra Question 227
Question: The sum of two forces is 18 N and resultant whose direction is at right angles to the smaller force is 12N. The magnitude of the two forces are
[AIEEE 2002]
Options:
A) 13, 5
B) 12, 6
C) 14, 4
D) 11, 7
Show Answer
Answer:
Correct Answer: A
Solution:
- $ P+Q=18,R=12,\theta =90^{o} $ , (say) $ \tan ,\theta =\tan 90^{o}=\infty $
$ \Rightarrow ,P+Q,\cos ,\alpha =0 $ ,
$ \therefore \cos \alpha =\frac{-P}{Q} $ Also, $ {{(12)}^{2}}=P^{2}+Q^{2}+2PQ\cos \alpha $ or $ 144=P^{2}+Q^{2}+(2P)(-P) $
$ \Rightarrow ,144=Q^{2}-P^{2}=(Q+P)(Q-P) $ or $ 144=18,(Q-P) $ or $ Q-P=8 $ After solving Q = 13, P = 5.
BETA
