Vector Algebra Question 366
Question: If three vectors a, b, c satisfy $ \mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0} $ and $ |\mathbf{a}|=3,, $ $ |\mathbf{b}|,=5, $ $ |\mathbf{c}|=7, $ then the angle between a and b is
[Kurukshetra CEE 1998; UPSEAT 2001; AIEEE 2002; MP PET 2002]
Options:
A) $ 30^{o} $
B) $ 45^{o} $
C) $ 60^{o} $
D) $ {90^{o}} $
Show Answer
Answer:
Correct Answer: C
Solution:
- Given, $ \mathbf{a}+\mathbf{b}+\mathbf{c}=0\Rightarrow \mathbf{a}+\mathbf{b}=-\mathbf{c} $ Squaring on both sides,
Þ $ |\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+2|\mathbf{a}||\mathbf{b}|\cos \theta =|-\mathbf{c}{{|}^{2}} $
$ \Rightarrow 9+25+30\cos \theta =49 $
Þ $ \cos \theta =\frac{1}{2}\Rightarrow \theta =60{}^\circ $ .
BETA
