A) \[\pi /2\]
B) \[\pi /3\]
C) \[\pi /4\]
D) \[\pi /6\]
Correct Answer: B
Solution :
[b] We know, if \[{{a}_{1}}x+{{b}_{1}}y+{{c}_{1}}z={{d}_{1}}\] and \[{{a}_{2}}x+{{b}_{2}}y+{{c}_{2}}z={{d}_{2}}\] Are two planes then angle between them is \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] Let q be the angle between given planes Here, \[{{a}_{1}}=2,{{b}_{1}}=-1,{{c}_{1}}=1;{{a}_{2}}=1,{{b}_{2}}=1,{{c}_{2}}=2\] \[\therefore \cos q=\frac{2\times 1+1\times (-1)+1\times 2}{\sqrt{4+1+1}\sqrt{1+1+4}}=\frac{3}{6}=\frac{1}{2}=\cos \frac{\pi }{3}\] \[\Rightarrow \theta =\frac{\pi }{3}\]
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