A) \[\frac{19}{5\sqrt{43}}\]
B) \[\frac{19}{3\sqrt{43}}\]
C) \[\frac{19}{2\sqrt{45}}\]
D) \[\frac{19}{6\sqrt{43}}\]
Correct Answer: A
Solution :
[a] \[(3\vec{a}-5\vec{b}).(2\vec{a}+\vec{b})=0\] Or \[6{{\left| {\vec{a}} \right|}^{2}}-5{{\left| {\vec{b}} \right|}^{2}}=7\vec{a}\cdot \vec{b}\] Also, \[(\vec{a}+4\vec{b}).(\vec{b}-\vec{a})=0\] Or \[-{{\left| {\vec{a}} \right|}^{2}}+4{{\left| {\vec{b}} \right|}^{2}}=3\vec{a}\cdot \vec{b}\] Or \[\frac{6}{7}{{\left| {\vec{a}} \right|}^{2}}-\frac{5}{7}{{\left| {\vec{b}} \right|}^{2}}=-\frac{1}{3}{{\left| {\vec{a}} \right|}^{2}}+\frac{4}{3}{{\left| {\vec{b}} \right|}^{2}}\] Or \[25{{\left| {\vec{a}} \right|}^{2}}=43{{\left| {\vec{b}} \right|}^{2}}\] \[\Rightarrow 3\vec{a}\cdot \vec{b}=-{{\left| {\vec{a}} \right|}^{2}}+4{{\left| {\vec{b}} \right|}^{2}}=\frac{57}{25}{{\left| {\vec{b}} \right|}^{2}}\] Or \[3\left| {\vec{a}} \right|\left| {\vec{b}} \right|\cos \theta =\frac{57}{25}{{\left| {\vec{b}} \right|}^{2}}\] Or \[\sqrt[3]{\frac{43}{25}}{{\left| {\vec{b}} \right|}^{2}}\cos \theta =\frac{57}{25}{{\left| {\vec{b}} \right|}^{2}}\] Or \[\cos \theta =\frac{19}{5\sqrt{43}}\]
You need to login to perform this action.
You will be redirected in
3 sec
