A) \[{{\cos }^{-1}}\left( \frac{2}{65} \right)\]
B) \[{{\cos }^{-1}}\left( \frac{1}{65} \right)\]
C) \[{{\cos }^{-1}}\left( \frac{3}{65} \right)\]
D) \[\frac{\pi }{3}\]
Correct Answer: B
Solution :
Direction ratios of both lines are \[{{a}_{1}}=5,{{b}_{1}}=-12,{{c}_{1}}=13\] and \[{{a}_{2}}=-3,{{b}_{2}}=4,{{c}_{2}}=5,\] then angle between them is given by \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] \[=\frac{5\times -3+4\times -12+13\times 5}{\sqrt{{{(5)}^{2}}+{{(-12)}^{2}}+{{(13)}^{2}}}\sqrt{{{(-3)}^{2}}+{{(4)}^{2}}+{{(5)}^{2}}}}\] \[=\frac{-15-48+65}{\sqrt{25+144+169}\sqrt{9+16+25}}\] \[=\frac{2}{13\sqrt{2}.5\sqrt{2}}\] \[\Rightarrow \] \[\cos \theta =\frac{1}{65}\] \[\Rightarrow \] \[\theta ={{\cos }^{-1}}\left( \frac{1}{65} \right)\]
You need to login to perform this action.
You will be redirected in
3 sec
