(Solved): A jogger travels a route that has two parts. The first is a displacement \( \vec{A} \) of \( 1.90 \ ...
A jogger travels a route that has two parts. The first is a displacement \( \vec{A} \) of \( 1.90 \mathrm{~km} \) due south, and the second involves a displacement \( \vec{B} \) that points due east. The resultant displacement \( \vec{A}+\vec{B} \) has a magnitude of \( 3.80 \mathrm{~km} \). (a) What is the magnitude of \( \vec{B} \), and (b) what is the direction of \( \vec{A}+\vec{B} \) as a positive angle relative to due south? Suppose that \( \vec{A} \cdot \vec{B} \) had a magnitude of \( 3.80 \mathrm{~km} \). (c) What then would be the magnitude of \( \vec{B} \), and (d) what is the direction of \( \vec{A}-\vec{B} \) relative to due south?