Given,
The magnitude of vector A, A=220 km
The direction of vector A, θ₁=32° north of west
The magnitude of vector B, B=140 Km
The direction of vector B, θ₂=65° east of north
(a)
(b)
The vector A is given by,

That is,

And vector B is given by,

Thus, vector D is given as

The magnitude of the vector D is given by,
![\begin{gathered} D=\sqrt[]{(-313.63)^2+57.65^2} \\ =318.88\text{ km} \end{gathered}](https://img.qammunity.org/2023/formulas/physics/college/i2jsvo5pef71p0179v1qxtcw4il2b3fnuu.png)
The direction of vector D is given by,

Therefore the magnitude of vector D is 318.88 km and the direction of the vector D is 10.41° north of the west.
The direction of the vector D is represented as,