A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
Correct Answer: C
Solution :
Let \[\theta \] be the angle between the lines. \[\therefore \] \[\cos \theta =\frac{{{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}}}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}}\] \[=\frac{4\times 3-3\times 4+5\times 5}{\sqrt{16+9+25}\sqrt{9+16+25}}\] \[=\frac{1}{2}=\cos \frac{\pi }{3}\] \[\Rightarrow \] \[\theta =\frac{\pi }{3}\] Let the length of the side be x.
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