Required information Margaret walks to the store using the following path: $0.650 \mathrm{mi}$ west, $0.420 \mathrm{mi}$ north, $0.110 \mathrm{mi}$ east. Assume north to be along the $+y$-axis and west to be along the $-x$-axis. Find the direction of the displacement vector. Enter the answer as an angle north of west north of west

Step 1 ：Margaret walks to the store using the following path: \(0.650 \mathrm{mi}\) west, \(0.420 \mathrm{mi}\) north, \(0.110 \mathrm{mi}\) east. We assume north to be along the \(+y\)-axis and west to be along the \(-x\)-axis.

Step 2 ：The displacement vector is the vector that 'points directly' from the start point to the end point. In this case, Margaret starts at some point, walks west, then north, then east. We can represent these movements as vectors and add them together to find the displacement vector.

Step 3 ：The westward movement is represented as a vector pointing in the negative x direction, the northward movement is represented as a vector pointing in the positive y direction, and the eastward movement is represented as a vector pointing in the positive x direction.

Step 4 ：We can add these vectors together to find the displacement vector. The x component of the displacement vector is the sum of the x components of the individual vectors, and the y component of the displacement vector is the sum of the y components of the individual vectors.

Step 5 ：Once we have the displacement vector, we can find its direction by calculating the angle it makes with the negative x axis (since west is along the negative x axis). This can be done using the arctangent function, which gives the angle a vector makes with the x axis.

Step 6 ：Given that west = \(0.65\), north = \(0.42\), east = \(0.11\), we find that dx = \(0.54\) and dy = \(0.42\).

Step 7 ：Calculating the angle, we find that it is approximately \(37.8749836510982\).

Step 8 ：Final Answer: The direction of the displacement vector is approximately \(\boxed{37.87^\circ}\) north of west.