Vector Algebra Question 369
Question: If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
[Kurukshetra CEE 1996; RPET 1996]
Options:
A) $ \sqrt{2} $
B) $ \sqrt{3} $
C) $ \frac{1}{\sqrt{3}} $
D) 1
Show Answer
Answer:
Correct Answer: B
Solution:
- Let $ |\mathbf{a}|=1 $ and $ |\mathbf{b}|=1 $ Also $ |\mathbf{a}+\mathbf{b}{{|}^{2}}=1^{2}\Rightarrow 1+1+2\cos \theta =1 $
$ \Rightarrow \theta =120{}^\circ $
$ \therefore ,|\mathbf{a}-\mathbf{b}{{|}^{2}}=1+1-2\cos \theta =3 $
$ \Rightarrow ,|\mathbf{a}-\mathbf{b}|,=\sqrt{3}. $
BETA
