Answer: 6.24 km
Explanation:
Given
The magnitude of the first vector(say) [tex]\left | a\right |=5\ km[/tex]
the magnitude of the second vector(say) [tex]\left | b\right |=7\ km[/tex]
the angle between them is [tex]120^{\circ}[/tex]
The resultant vector magnitude is given by
[tex]\left | \vec{R}\right |=\sqrt{a^2+b^2+2ab\cos \theta}[/tex]
[tex]\left | \vec{R}\right |=\sqrt{5^2+7^2+2\times 5\times 7\cdot \cos 120^{\circ}}\\\left | \vec{R}\right |=\sqrt{74-35}=\sqrt{39}\\\left | \vec{R}\right |=6.24\ km[/tex]
