Question

In a rectangle $ABCD$ where $A$ is origin as shown in the figure, what is $\overrightarrow{AB}+\overrightarrow{AD}$ ?

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

Answer 1

The correct option is B $5\hat{i}+4\hat{j}$

The length $AB$ and $AD$ can be written in the vector form as
$\overrightarrow{AB}=5\hat{i}+0\hat{j}$ and $\overrightarrow{AD}=0\hat{i}+4\hat{j}$
Thus, $\overrightarrow{AB}+\overrightarrow{AD}=(5\hat{i}+0\hat{j})+(0\hat{i}+4\hat{j})=5\hat{i}+4\hat{j}$