Define the displacement vectors in component form.

Here are the solutions to the problems:

1. Resultant Displacement by Components

Step 1: Define the displacement vectors in component form.
Let north be the positive y-direction and east be the positive x-direction.

• $\vec{d_1} = 4.25 \text{ km south} = (0)\hat{i} + (-4.25)\hat{j} \text{ km}$
• $\vec{d_2} = 2.75 \text{ km west} = (-2.75)\hat{i} + (0)\hat{j} \text{ km}$
• $\vec{d_3} = 1.50 km north =