Question

In the cube of side $‘a^{\prime }$ shown in the figure, the vector from the central point of the face $ABOD$ to the central point of the face $BEFO$ will be

• A. $\frac{1}{2}a(\hat{i}-\hat{k})$
• B. $\frac{1}{2}a(\hat{j}-\hat{i})$
• C. $\frac{1}{2}a(\hat{k}-\hat{i})$
• D. $\frac{1}{2}a(\hat{j}-\hat{k})$

Answer 1

The correct option is B $\frac{1}{2}a(\hat{j}-\hat{i})$

From figure the position vector of $G$
$\overrightarrow{r_G}=\frac{a}{2}(\hat{k}+\hat{i})$
The position vector of $H$
$\overrightarrow{r_H}=\frac{a}{2}(\hat{k}+\hat{j})$
$\overrightarrow{r_{HG}}=\overrightarrow{r_H}-\overrightarrow{r_G}$ $=\frac{a}{2}(\hat{j}-\hat{i})$
Final Answer: $\left(b\right)$