A) \[{{\cos }^{-1}}\left( \frac{1}{18} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{1}{3\sqrt{6}} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{1}{6\sqrt{3}} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{1}{3\sqrt{2}} \right)\]
Correct Answer: C
Solution :
\[{{L}_{1}}:\frac{x-1}{-2}=\frac{y-0}{1}=\frac{z+1}{1};\] \[{{L}_{2}}:\frac{x-4}{1}=\frac{y-5}{4}=\frac{z+2}{-1}\] \[{{\vec{V}}_{1}}=-2\hat{i}+\hat{j}+\hat{k},{{\vec{V}}_{2}}=\hat{i}+4\hat{j}-\hat{k}\] \[\cos \theta =\left| \frac{-2+4-1}{\sqrt{6}.\sqrt{18}} \right|=\frac{1}{6\sqrt{3}}\Rightarrow \theta ={{\cos }^{-1}}\left( \frac{1}{6\sqrt{3}} \right)\]You need to login to perform this action.
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