c
\(S_x = (6 -4) cos 45°\) \(\hat i\) \( = 2 \times \frac{1}{{\sqrt 2 }}\, = \,\sqrt 2 \,km\)

\(S_y = (6 + 4) sin 45°\)\(\hat j\) \( = 10 \times \frac{1}{{\sqrt 2 }} = 5\sqrt 2 \,km\)

\(|\overrightarrow s |\, = \sqrt {{s_x}^2 + {s_y}^2} \)\( = \sqrt {{{\left( {\sqrt 2 } \right)}^2} + {{\left( {5\sqrt 2 } \right)}^2}} \) = \(\sqrt {52} \,\,km\)