question_answer

  Find the direction cosines of the two lines which are connected by the relations \[l-5m+3n=0\] and \[7{{l}^{2}}+5{{m}^{2}}-3{{n}^{2}}=0\].

A)  \[\pm \frac{1}{\sqrt{14}},\pm \frac{2}{\sqrt{14}},\pm \frac{3}{\sqrt{14}}\] and \[\pm \frac{-1}{\sqrt{6}},\pm \frac{1}{6},\pm \frac{2}{\sqrt{6}}\]

B)  \[\pm \frac{1}{\sqrt{13}},\pm \frac{2}{\sqrt{13}},\pm \frac{3}{\sqrt{13}}\] and \[\pm \frac{1}{\sqrt{5}},\pm \frac{1}{\sqrt{5}},\pm \frac{1}{\sqrt{5}}\]

C)  \[\pm \frac{1}{\sqrt{11}},\pm \frac{3}{\sqrt{11}},\pm \frac{2}{\sqrt{11}}\] and \[\pm \frac{1}{\sqrt{6}},\pm \frac{1}{\sqrt{6}},\pm \frac{3}{\sqrt{6}}\]

D)  \[\pm \frac{1}{\sqrt{13}},\pm \frac{2}{\sqrt{13}},\pm \frac{3}{\sqrt{13}}\] and \[\pm \frac{1}{\sqrt{5}},\pm \frac{1}{\sqrt{5}},\pm \frac{2}{\sqrt{5}}\]

E)  None of these