A) \[{{\cos }^{-1}}\left( \frac{13}{9\sqrt{38}} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{26}{9\sqrt{38}} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{4}{\sqrt{38}} \right)\]
D) \[{{\cos }^{-1}}\left( \frac{2\sqrt{2}}{\sqrt{19}} \right)\]
Correct Answer: B
Solution :
\[\cos \theta =\frac{2\times (-1)+5\times 8+(-3)\times 4}{\sqrt{{{2}^{2}}+{{5}^{2}}+{{(-3)}^{2}}}\sqrt{{{(-1)}^{2}}+{{8}^{2}}+{{4}^{2}}}}\] \[\cos \theta =\frac{-2+40-12}{9\sqrt{38}}\]\[=\left( \frac{26}{9\sqrt{38}} \right)\] \ \[\theta ={{\cos }^{-1}}\left( \frac{26}{9\sqrt{38}} \right)\].
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