The vectors $\rm \vec a, \vec b\ and\ \vec c$ are of the same length. If taken pairwise they form equal angles. If $\rm \vec a=̂ i+̂ j\ and \ \vec b=̂ j+̂ k,$ then what can $\vec c$ be equal to? 

I. î + k̂ 

II. $\rm \frac{-\hat i+4\hat j-\hat k}{3}$

Select the correct answer using the code given below. 

If the direction cosines <l, m, n> of a line are connected by relation $l + 2m + n = 0, 2l - 2m + 3n = 0$, then what is the value of $l^{2} + m^{2} - n^{2}$?