Question:
If the middle points of sides BC, CA and AB of triangle ABC are respectively D, E, F. If the position vectors of A, B, C are \(\hat{i}+\hat{j},\;\hat{j}+\hat{k},\;\hat{k}+\hat{i}\) respectively, then the position vector of the centre of triangle DEF is
If the middle points of sides BC, CA and AB of triangle ABC are respectively D, E, F. If the position vectors of A, B, C are \(\hat{i}+\hat{j},\;\hat{j}+\hat{k},\;\hat{k}+\hat{i}\) respectively, then the position vector of the centre of triangle DEF is
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The centroid of the medial triangle is same as the original triangle.
Updated On: Mar 24, 2026
- \(\dfrac{1}{3}(\hat{i}+\hat{j}+\hat{k})\)
- \(\hat{i}+\hat{j}+\hat{k}\)
- \(2(\hat{i}+\hat{j}+\hat{k})\)
- \(\dfrac{2}{3}(\hat{i}+\hat{j}+\hat{k})\)
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The Correct Option is A
Solution and Explanation
Step 1: Coordinates of centroid of ABC: \[ \frac{A+B+C}{3} \]
Step 2: Triangle DEF has same centroid as ABC.
Step 3: \[ \frac{(\hat{i}+\hat{j})+(\hat{j}+\hat{k})+(\hat{k}+\hat{i})}{3} =\frac{1}{3}(\hat{i}+\hat{j}+\hat{k}) \]
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