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Q.
The ($x$, $y$, $z$) coordinates of two points $A$ and $B$ are given respectively as ($0$, $4$, $-2$) and ($-2$, $8$, $-4$). The displacement vector from $A$ to $B$ is
Motion in a Plane
Solution:
Here, $\vec{r}_{A}=0\hat{i}+4\hat{j}-2\hat{k}$,
$\vec{r}_{B}=-2\hat{i}+8\hat{j}-4\hat{k}$
Displacement vector from $A$ to $B$ is given by
$\vec{r}=\vec{r}_{B}-\vec{r}_{A}$
$=\left(-2\hat{i}+8\hat{j}-4\hat{k}\right)-\left(0\hat{i}+4\hat{j}-2\hat{k}\right)$
$=-2\hat{i}+4\hat{j}-2\hat{k}$