A) \[{{\cos }^{-1}}\frac{3\sqrt{2}}{10}\]
B) \[{{\cos }^{-1}}\frac{19\sqrt{2}}{30}\]
C) \[{{\cos }^{-1}}\frac{9\sqrt{2}}{20}\]
D) \[{{\cos }^{-1}}\frac{3\sqrt{2}}{5}\]
Correct Answer: A
Solution :
Angle between two planes is, \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\,\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] \[\cos \theta =\frac{(1)\,(-5)\,+(2)\,(3)+(2)\,(4)}{\sqrt{{{1}^{2}}+{{2}^{2}}+{{2}^{2}}}\sqrt{{{(-5)}^{2}}+{{3}^{2}}+{{4}^{2}}}}\] \[\cos \theta =\frac{3\sqrt{2}}{10}\Rightarrow \theta ={{\cos }^{-1}}\left( \frac{3\sqrt{2}}{10} \right)\].
You need to login to perform this action.
You will be redirected in
3 sec
