A) \[\frac{1}{3}(\hat{i}+\hat{j}+\hat{k})\]
B) \[(\hat{i}+\hat{j}+\hat{k})\]
C) \[2(\hat{i}+\hat{j}+\hat{k})\]
D) \[\frac{2}{3}(\hat{i}+\hat{j}+\hat{k})\]
Correct Answer: D
Solution :
[d] The position vector of points D, E, F are respectively \[\frac{\hat{i}+\hat{j}}{2}+\hat{k},\hat{i}+\frac{\hat{k}+\hat{j}}{2}\] and \[\frac{\hat{i}+\hat{k}}{2}+\hat{j}\] So, position vector of centre of \[\Delta DEF\] \[=\frac{1}{3}\left[ \frac{\hat{i}+\hat{j}}{2}+\hat{k}+\hat{i}\frac{\hat{k}+\hat{j}}{2}+\frac{\hat{i}+\hat{k}}{2}+\hat{j} \right]\] \[=\frac{2}{3}\left[ \hat{i}+\hat{j}+\hat{k} \right]\]You need to login to perform this action.
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