Question

A student bikes to school by traveling first dN = 1.00 miles north, then dW = 0.600 miles west, and finally dS = 0.200 miles south. Take the north direction as the positive y direction and east as positive x. The origin is still where the student starts biking. Let d⃗ N be the displacement vector corresponding to the first leg of the student's trip. Express d⃗ N in component form

Answer 1

Refer to the diagram shown below.

Define unit vectors along the x and y axes as respectively $\hat{i} \, and \, \hat{j}.$

Then the three successive displacements, written in component form, are respectively
$\vec{dN} = 1.0 \, \hat{j} \\ \vec{dW} = -0.6 \, \hat{i} \\ \vec{dS} = -0.2 \, \hat{j}$

The total displacement for the first leg of the trip is
$\vec{d} = \vec{dN} + \vec{dW} + \vec{dS} \\ \vec{d}= 1.0\hat{j}-0.6\hat{i}-0.2\hat{j} \\ \vec{d}=-0.6\hat{i}+0.8\hat{j}$

Answer:
$\vec{d} = -0.6\hat{i}+0.8\hat{j}$   or  (-0.6, 0.8)