A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) None of the above
Correct Answer: A
Solution :
[a] The given lines are:- \[\frac{x-2}{1}=\frac{y-(-1)}{-2}=\frac{z-(-2)}{1}\] and \[\frac{x-1}{1}=\frac{y-\left( -\frac{3}{2} \right)}{\frac{3}{2}}=\frac{z-(-5)}{2}\] Dr?s of 1st line are:- \[{{a}_{1}}=1,{{b}_{1}}=-2,{{c}_{1}}=1\] Dr?s of IInd line are:- \[{{a}_{2}}=2,{{b}_{2}}=3,{{c}_{2}}=4\] Let \['\theta '\] be the angle b/w two lines, then. \[\cos \theta =\frac{\left| {{a}_{1}}{{a}_{2}}+{{b}_{1}}{{b}_{2}}+{{c}_{1}}{{c}_{2}} \right|}{\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}.\sqrt{a_{2}^{2}+b_{2}^{2}+c_{2}^{2}}}\] \[\cos \theta =0\] \[\Rightarrow \theta =\frac{\pi }{2}\]
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