Vector Algebra Question 329
Question: If $ |\mathbf{a}+\mathbf{b}|>|\mathbf{a}-\mathbf{b}|, $ then the angle between a and b is
Options:
A) Acute
B) Obtuse
C) $ \frac{\pi }{2} $
D) $ \pi $
Show Answer
Answer:
Correct Answer: A
Solution:
- $ |\mathbf{a}+\mathbf{b}|,>,|\mathbf{a}-\mathbf{b}| $ Squaring both sides, we get $ a^{2}+b^{2}+2\mathbf{a},.,\mathbf{b},>,a^{2}+b^{2}-2\mathbf{a},.,\mathbf{b} $ $ $
Þ $ 4\mathbf{a}.\mathbf{b}>0 $
Þ $ \cos \theta >0 $ . Hence $ \theta ,<,90{}^\circ $ , (acute).
BETA
