91Ó°ÊÓ

• Starting coordinates$(0,0,0)$
• Finishing coordinates $(-2\mathrm{cm},4\mathrm{cm},-4\mathrm{cm})$
• Coordinates that are not allowed$(-5\mathrm{cm},-1 \mathrm{cm},-1 \mathrm{cm})\mathrm{and}(5\mathrm{cm},2\mathrm{cm},-1\mathrm{cm})$

The vector quantity has magnitude as well as direction. The vectors cannot be added using simple mathematical operations. Two vectors can be added only when they are of the same type and nature. To add the vectors, we can use the laws of vector addition.

Formula:

$\stackrel{→}{\mathrm{A}}+\stackrel{→}{\mathrm{B}}=\stackrel{→}{\mathrm{C}}$

Let us start with displacement $p⃗=-7\hat{i}+2\hat{j}-3\hat{k}$

After that, we can use displacement$s⃗=3\hat{i}+5\hat{j}-3\hat{k}$

By adding these two displacements we can reach a point say A.

role="math" localid="1657007161563" $$\begin{gathered} p⃗+s⃗=(-7\hat{i}+2\hat{j}-3\hat{k})+(3\hat{i}+5\hat{j}-3\hat{k}) \\ p⃗+s⃗=(-4\hat{i}+7\hat{j}-"6\hat{k}) \end{gathered}$$

Now, we will use displacement

$$\begin{gathered} \mathrm{r}⃗=(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}) \\ \stackrel{→}{\mathrm{A}}+\stackrel{→}{\mathrm{r}}=(-4\hat{\mathrm{i}}+7\hat{\mathrm{j}}-6\hat{\mathrm{k}})+(2\hat{\mathrm{i}}-3\hat{\mathrm{j}}+2\hat{\mathrm{k}}) \\ \stackrel{→}{\mathrm{A}}+\stackrel{→}{\mathrm{r}}=(-2\hat{\mathrm{i}}+4\hat{\mathrm{j}}-4\hat{\mathrm{k}}) \end{gathered}$$

We can ensure to avoid the points$(-5\mathrm{cm},-1 \mathrm{cm},-1 \mathrm{cm})$ as we have not moved to negative y axis.

And also, it is ensured that we cannot come across point$(5\mathrm{cm},2\mathrm{cm},-1\mathrm{cm})$as we have not moved to positive x axis.

Thus, the sequence of the displacements will be $\stackrel{→}{p}-\stackrel{→}{s}-\stackrel{→}{r}$.