A) \[\frac{a}{5}\left( \hat{i}-\hat{j} \right)\]
B) \[\frac{a}{5}\left( \hat{i}+\hat{j} \right)\]
C) Zero
D) \[a\left( \hat{i}+\hat{j} \right)\]
Correct Answer: A
Solution :
\[{{\vec{a}}_{A}}=-a\hat{i}\] \[{{\vec{a}}_{B}}=a\hat{j}\] \[{{\vec{a}}_{C}}=a\hat{i}\] \[{{\vec{a}}_{D}}=-a\hat{j}\] \[{{\vec{a}}_{cm}}=\frac{{{m}_{a}}{{{\vec{a}}}_{a}}+{{m}_{b}}{{{\vec{a}}}_{b}}+{{m}_{c}}{{{\vec{a}}}_{c}}+{{m}_{d}}{{{\vec{a}}}_{d}}}{{{m}_{a}}+{{m}_{b}}+{{m}_{c}}+{{m}_{d}}}\] \[{{\vec{a}}_{cm}}=\frac{-ma\hat{i}+2ma\hat{j}+3ma\hat{i}-4ma\hat{j}}{10m}\] \[=\frac{2ma\hat{i}-2ma\hat{j}}{10m}\] \[=\frac{a}{5}\hat{i}-\frac{a}{5}\hat{j}\] \[=\frac{a}{5}\left( \hat{i}-\hat{j} \right)\]You need to login to perform this action.
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