A) \[{{\cos }^{-1}}\left( \frac{49}{36} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{18\sqrt{2}}{35} \right)\]
C) \[96{}^\circ \]
D) \[{{\cos }^{-1}}\left( \frac{18}{35} \right)\]
Correct Answer: B
Solution :
\[\cos \theta =\left| \frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}} \right|\] \[\cos \theta =\left| \frac{(2)\,(3)\,+\,(3)\,(-4)\,+(-6)\,(5)}{\sqrt{{{2}^{2}}+{{3}^{2}}+{{(-6)}^{2}}}.\,\sqrt{{{3}^{2}}+{{(-4)}^{2}}+{{(5)}^{2}}}} \right|\] \[\cos \theta =\frac{18\sqrt{2}}{35}\] Þ \[\theta ={{\cos }^{-1}}\left( \frac{18\sqrt{2}}{35} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
