Define unit vectors as follows:
[tex]\hat{i}[/tex] is in the eastern direction.
[tex]\hat{j}[/tex] is in the northern direction.
The position of the first bird is
[tex]\vec{a} = -3.6 \, \hat{i} + 1.8 \, \hat{j}[/tex]
The position of the second bird is
[tex]\vec{b} = - 1.8 \, \hat{i} + 3.6 \, \hat{j}[/tex]
Let θ = the angle between the net displacement vector for the two birds.
By definition,
[tex]\vec{a} . \vec{b} = |a| |b| cos\theta \\\\ \theta = cos^{-1} ( \frac{\vec{a}.\vec{b}}{|a||b|} )[/tex]
[tex]\vec{a}.\vec{b} = (-3.6)(-1.8)+(3.6)(1.8) = 12.96[/tex]
[tex]|a| = \sqrt{3.24+12.96} =4.025[/tex]
Similarly,
|b| = 4.025
Therefore
[tex]\theta = cos^{-1} \frac{12.96}{4.025^{2}} =36.9^{o}[/tex]
Answer: 36.9°
