Question

If Sunil moves along a rectangular path from point $A(0,0)$ as shown in the figure to point $C$ of the rectangle, what is his displacement vector. Take line $AB$ as $x$-axis and $AD$ as $y$-axis.The dimensions of the rectangle are mentioned.

• A. 3$\hat{i}$+4$\hat{j}$
• B. $0$
• C. 4$\hat{i}$+3$\hat{j}$
• D. 4$\hat{i}$+5$\hat{j}$

Answer 1

The correct option is C 4$\hat{i}$+3$\hat{j}$

From definition,
The displacement vector is difference between the position vector of point $C$ and point $A$.
With reference to $A$ the coordinate of point $C$ is $(4,3)$
Position vector of $C$ is $\overrightarrow{r_C}=$ 4$\hat{i}$+3$\hat{j}$
Hence, displacement vector ${\overrightarrow{V}}_{disp}$
= $\overrightarrow{r_C}-\overrightarrow{r_A}$= (4$\hat{i}$+3$\hat{j}$) - (0$\hat{i}$+0$\hat{j}$)
= 4$\hat{i}$+3$\hat{j}$