Vector Algebra Question 214
Question: If $ \hat{a},\hat{b} $ and $ \hat{c} $ are three unit vectors inclined to each other at an angle $ \theta $ , then the maximum value of $ \theta $ is
Options:
A) $ \frac{\pi }{3} $
B) $ \frac{\pi }{2} $
C) $ \frac{2\pi }{3} $
D) $ \frac{5\pi }{6} $
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ {{(\hat{a}+\hat{b}+\hat{c})}^{2}}\ge 0 $ $ 3+2(\hat{a}.\hat{b}+\vec{b}.\hat{c}+\vec{c}.\vec{a})\ge 0 $ $ 3+6\cos \theta \ge 0 $ $ \cos \theta \ge -\frac{1}{2} $
$ \Rightarrow \theta =\frac{2\pi }{3} $
BETA
