Question

In the cube of side $'a'$ 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. $\frac{1}{2} a \left(\hat{i} -\hat{k}\right)$
• B. $\frac{1}{2} a \left(\hat{j} -\hat{i}\right)$
• C. $\frac{1}{2} a \left(\hat{k} -\hat{i}\right)$
• D. $\frac{1}{2} a \left(\hat{j} -\hat{k}\right)$

Answer 1

Answer: (B)

$\frac{1}{2} a \left(\hat{j} -\hat{i}\right)$

Answer 2

$\vec{r}_{g} = \frac{a}{2} \hat{i} + \frac{a}{2} \hat{k}$
$\vec{r}_{H} =\frac{a}{2} \hat{j} + \frac{a}{2} \hat{k}$
$\vec{ r}_{H} - \vec{r}_{g} = \frac{a}{2} \left(\hat{j} - \hat{i}\right)$