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3-1.Vectors
medium
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
$\frac{1}{2}\,a\,\left( {\hat k - \hat i} \right)$
B
$\frac{1}{2}\,a\,\left( {\hat i - \hat k} \right)$
C
$\frac{1}{2}\,a\,\left( {\hat j - \hat i} \right)$
D
$\frac{1}{2}\,a\,\left( {\hat j - \hat k} \right)$
(JEE MAIN-2019)
Solution
Position vector of $G$ is $\overrightarrow{O G}=\frac{a \vec{i}}{2}+\frac{a}{2} \vec{k}$
Position vector of $H$ is $\overrightarrow{O H}=\frac{a}{2} \vec{j}+\frac{a}{2} \vec{k}$
$\overrightarrow{G H}=\frac{a}{2}(\vec{j}-\vec{i})$
Standard 11
Physics
