Which of these triples can be the direction cosines of a line?

Explanation

1. 01

   Direction cosines must satisfy $l^{2} + m^{2} + n^{2} = 1$.

2. 02

   For $\frac{1}{2}, -\frac{1}{2}, \frac{1}{\sqrt{2}}$: $\frac{1}{4} + \frac{1}{4} + \frac{1}{2} = 1$; the other triples give $\frac{3}{8}$, $\frac{5}{4}$ and $\frac{2}{3}$.