A) \[\frac{\pi }{6}\]
B) \[\frac{2\pi }{3}\]
C) \[\frac{5\pi }{3}\]
D) \[\frac{\pi }{3}\]
Correct Answer: D
Solution :
\[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}.|\overrightarrow{a}|=3,|\overrightarrow{b}|=5,|\overrightarrow{c}|=7\] \[\therefore \] \[\overrightarrow{c}=-(\overrightarrow{a}+\overrightarrow{b})\] \[\Rightarrow \] \[|\overrightarrow{c}{{|}^{2}}=|-(\overrightarrow{a}+\overrightarrow{b}){{|}^{2}}\] \[\Rightarrow \] \[|\overrightarrow{c}{{|}^{2}}=|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+2|\overrightarrow{a}|.|\overrightarrow{b}|\cos \theta \] \[\Rightarrow \] \[{{(7)}^{2}}={{(3)}^{2}}+{{(5)}^{2}}+2(3)(5)\cos \theta \] \[\Rightarrow \] \[49-9-25=30\cos \theta \] \[\Rightarrow \] \[\cos \theta =\frac{15}{30}\] \[\Rightarrow \] \[\cos \theta =\frac{1}{2}=\cos \frac{\pi }{3}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\]
You need to login to perform this action.
You will be redirected in
3 sec
