Answer
$ (-2\hat{i}+6\hat{j}-10\hat{k})\ m$
Work Step by Step
Given:
Displacement $\vec{\Delta r} = 2\hat{i}-3\hat{j}+6\hat{k}$
Ending position vector $\vec{r_f}=3\hat{j}-4\hat{k}$
Let the initial position vector be $r_i$.
We know that:
$\vec{\Delta r }= \vec{r_f}-\vec{r_i}$
This can be rearranged as:
$\vec{r_i} =\vec{r_f} - \vec{\Delta r}$
Substituting and solving:
$\vec{\Delta r} =3\hat{j}-4\hat{k} - (2\hat{i}-3\hat{j}+6\hat{k})$
$\vec{\Delta r} = (-2\hat{i}+6\hat{j}-10\hat{k})\ m$
