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

• A. \(\dfrac{1}{3}(\hat{i}+\hat{j}+\hat{k})\)
• B. \(\hat{i}+\hat{j}+\hat{k}\)
• C. \(2(\hat{i}+\hat{j}+\hat{k})\)
• D. \(\dfrac{2}{3}(\hat{i}+\hat{j}+\hat{k})\)

Hint:

The centroid of the medial triangle is same as the original triangle.

Answer 1

The Correct Option is A