A) \[{{\cos }^{-1}}\left( \frac{1}{3} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{4}{21} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{4}{9} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{7}{\sqrt{84}} \right)\]
Correct Answer: C
Solution :
[c] \[2{{x}^{2}}-2{{y}^{2}}+4{{z}^{2}}+(6xz+2yz+3xy)=0\] or \[2{{x}^{2}}+x(6z+3y)-2{{y}^{2}}+4{{z}^{2}}+2yz=0\] \[x=\frac{-(6z+3y)\pm \sqrt{36{{z}^{2}}+9{{y}^{2}}+36yz-8(-2{{y}^{2}}+4{{z}^{2}}+2yz)}}{4}\]\[x=\frac{-(6z+3y)\pm \sqrt{{{(2z+5y)}^{2}}}}{4}\] \[\Rightarrow x=\frac{-(6z+3y)\pm (2z+5y)}{4}\] or \[2x-y+2z=0,x+2y+2z=0\] \[\therefore \] Angle between planes is \[{{\cos }^{-1}}\left( \frac{4}{9} \right).\]
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