Vector Algebra Question 375
Question: If a and b are two unit vectors such that $ \mathbf{a}+2,\mathbf{b} $ and $ 5a-4b $ are perpendicular to each other, then the angle between a and b is
[IIT Screening 2002]
Options:
A) $ 45^{o} $
B) $ 60^{o} $
C) $ {{\cos }^{-1}}( \frac{1}{3} ) $
D) $ {{\cos }^{-1}}( \frac{2}{7} ) $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ (\mathbf{a}+2\mathbf{b}),.,(5\mathbf{a}-4\mathbf{b})=0 $ or $ 5{{\mathbf{a}}^{2}}+6\mathbf{a},.,\mathbf{b}-8{{\mathbf{b}}^{2}}=0 $ or $ 6,\mathbf{a},.,\mathbf{b}=3, $ $ (\because {{\mathbf{a}}^{2}}=1,,{{\mathbf{b}}^{2}}=1) $
$ \therefore ,\mathbf{a},.,\mathbf{b}=\frac{1}{2} $ or $ |\mathbf{a}||\mathbf{b}|\cos \theta =\frac{1}{2} $
$ \therefore ,\cos \theta =\frac{1}{2},,,\therefore \theta =60^{o}. $
BETA
