Question

The $(x,y,z)$coordinates of two points $A$ and $B$ are given respectively, as $(0,3,–1)$ and $(–2,6,4)$. The displacement vector from $A$ to $B$ may be given by

• A. $-2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+4\hat{\mathrm{k}}$
• B. $-2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+3\hat{\mathrm{k}}$
• C. $-2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$
• D. $2\hat{\mathrm{i}}+3\hat{\mathrm{j}}-5\hat{\mathrm{k}}$

Answer 1

The correct option is C

$-2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$

Explanation of the correct option.

Given : ${\mathrm{r}}_A=3\hat{\mathrm{j}}-\hat{\mathrm{k}}$, ${\mathrm{r}}_B=-2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+4\hat{\mathrm{k}}$

Since the displacement vector $r_{AB}$ is given by, $r_B-r_A$

$$\begin{gathered} {\mathrm{r}}_{\mathrm{AB}}=\left(-2\hat{\mathrm{i}}+6\hat{\mathrm{j}}+4\hat{\mathrm{k}}\right)-(3\hat{\mathrm{j}}-\hat{\mathrm{k}}) \\ \Rightarrow {\mathrm{r}}_{\mathrm{AB}}=-2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+5\hat{\mathrm{k}} \end{gathered}$$

Therefore, the displacement vector from $A$ to $B$ is $-2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+5\hat{\mathrm{k}}$.

Hence option C is the correct option.