A) all are acute angles
B) all are right angles
C) at least one is obtuse angle
D) none of these
Correct Answer: C
Solution :
[c] \[{{\left| \vec{a}+\vec{b}+\vec{c} \right|}^{2}}=1\] \[\Rightarrow {{\left| {\vec{a}} \right|}^{2}}+{{\left| {\vec{b}} \right|}^{2}}+{{\left| {\vec{c}} \right|}^{2}}+2\left| {\vec{a}} \right|\left| {\vec{b}} \right|\cos {{\theta }_{1}}\] \[+2\left| {\vec{b}} \right|\left| {\vec{c}} \right|\cos {{\theta }_{2}}+2\left| {\vec{c}} \right|\left| {\vec{a}} \right|\cos {{\theta }_{3}}=1\] \[\Rightarrow \cos {{\theta }_{1}}+\cos {{\theta }_{2}}+\cos {{\theta }_{3}}=-1\] Hence, one of \[{{\theta }_{1}},{{\theta }_{2}}\]and \[{{\theta }_{3}}\]should be an obtuse angle.You need to login to perform this action.
You will be redirected in
3 sec