A) 0
B) \[30{}^\circ \]
C) \[45{}^\circ \]
D) \[60{}^\circ \]
E) \[90{}^\circ \]
Correct Answer: D
Solution :
\[\because \] \[\overrightarrow{a}+\overrightarrow{b}+\overrightarrow{c}=\overrightarrow{0}\] \[\Rightarrow \] \[\overrightarrow{a}+\overrightarrow{b}=-\overrightarrow{c}\] \[\Rightarrow \] \[{{(\overrightarrow{a}+\overrightarrow{b})}^{2}}={{(-\overrightarrow{c})}^{2}}\] \[\Rightarrow \] \[{{\overrightarrow{a}}^{2}}+{{\overrightarrow{b}}^{2}}+2\overrightarrow{a}.\overrightarrow{b}={{\overrightarrow{c}}^{2}}\] \[\Rightarrow \] \[|\overrightarrow{a}{{|}^{2}}+|\overrightarrow{b}{{|}^{2}}+2|\overrightarrow{a}||\overrightarrow{b}|=\cos \theta =|\overrightarrow{c}{{|}^{2}}\] \[\Rightarrow \] \[9+25+2\times 3\times 5\cos \theta =49\] \[\Rightarrow \] \[\cos \theta =\frac{15}{30}=\frac{1}{2}\] \[\Rightarrow \] \[\theta =60{}^\circ \]
You need to login to perform this action.
You will be redirected in
3 sec
