Answer
The x component of $\Delta r$ is $~~-2~m$
Work Step by Step
In part (a), we found that $r_i = (7~m)\hat{i}+(1~m)\hat{j}-(2~m)\hat{k}$
In part (b), we found that $r_f = (5~m)\hat{i}- (3~m)\hat{j}+(1~m)\hat{k}$
We can find $\Delta r$:
$\Delta r = r_f-r_i = -(2~m)\hat{i}-(4~m)\hat{j}+(3~m)\hat{k}$
The x component of $\Delta r$ is $~~-2~m$
