In the cube of side $^{'} a^{'}$ shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be

\frac{1}{2} a (^i -^k)

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\frac{1}{2} a (^j -^i)

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\frac{1}{2} a (^k -^i)

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\frac{1}{2} a (^j -^k)

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Solution

The correct option is B $\frac{1}{2} a (^j -^i)$
${\to r}_{g} = \frac{a}{2}^i + \frac{a}{2}^k$
${\to r}_{H} = \frac{a}{2}^j + \frac{a}{2}^k$
${\to r}_{H} - {\to r}_{g} = \frac{a}{2} (^j -^i)$ .

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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

The correct option is B 12a(^j−^i)→rg=a2^i+a2^k→rH=a2^j+a2^k→rH−→rg=a2(^j−^i).

In the cube of side $^{'} a^{'}$ shown in the figure, the vector from the central point of the face $A B O D$ to the central point of the face $B E F O$ will be

The correct option is B $\frac{1}{2} a (^j -^i)$
${\to r}_{g} = \frac{a}{2}^i + \frac{a}{2}^k$
${\to r}_{H} = \frac{a}{2}^j + \frac{a}{2}^k$
${\to r}_{H} - {\to r}_{g} = \frac{a}{2} (^j -^i)$ .