Vector Algebra Question 350
Question: If q be the angle between the unit vectors a and b, then $ \mathbf{a}-\sqrt{2},\mathbf{b} $ will be a unit vector if $ \theta = $
Options:
A) $ \frac{\pi }{6} $
B) $ \frac{\pi }{4} $
C) $ p\mathbf{i}+q\mathbf{j}+r\mathbf{k} $
D) $ \frac{2\pi }{3} $
Show Answer
Answer:
Correct Answer: B
Solution:
- $ {{(\mathbf{a}-\sqrt{2}\mathbf{b})}^{2}}=1\Rightarrow 1+2-2\sqrt{2}\mathbf{a},.,\mathbf{b}=1 $
$ \Rightarrow \mathbf{a},.,\mathbf{b}=\frac{1}{\sqrt{2}}\Rightarrow \cos \theta =\frac{1}{\sqrt{2}}\Rightarrow \theta =\frac{\pi }{4}. $
BETA
