The angle between the lines whose direction cosines satisfy the equations \[l+m+n=0\], \[{{l}^{2}}+{{m}^{2}}-{{n}^{2}}=0\] is given by [MP PET 1993; RPET 2001]

• A.                                                               \[\frac{2\pi }{3}\]
• B.                                                               \[\frac{\pi }{6}\]
• C.                                                               \[\frac{5\pi }{6}\]
• D.                                                               \[\frac{\pi }{3}\]