Vector Algebra Question 325
Question: If $ |\mathbf{a}|+|\mathbf{b}|,=,|\mathbf{c}| $ and $ \mathbf{a}+\mathbf{b}=\mathbf{c}, $ then the angle between a and b is
Options:
A) $ \frac{\pi }{2} $
B) $ \pi $
C) 0
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
- $ \mathbf{a}+\mathbf{b}=\mathbf{c}\Rightarrow ,|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+2\mathbf{a},.,\mathbf{b}=,|\mathbf{c}{{|}^{2}} $ and $ |\mathbf{a}|+|\mathbf{b}|,=,|\mathbf{c}| $
$ \Rightarrow ,|\mathbf{a}{{|}^{2}}+|\mathbf{b}{{|}^{2}}+2|\mathbf{a}||\mathbf{b}|,=,|\mathbf{c}{{|}^{2}} $
$ \therefore ,\mathbf{a},.,\mathbf{b}=,|\mathbf{a}||\mathbf{b}|\Rightarrow \cos \theta =1 $
Þ $ \theta =0. $
BETA
