Question

Given orthocentre $\overline{H}$ and circumcentre $\overline{C}$ for a triangle as $2\hat{i}+3\hat{j}and4\hat{i}+5\hat{k}$.Then the centroid of triangle can be given by,

• A. $\frac{10\hat{i}-13\hat{j}}{3}$
• B. $\frac{-10\hat{i}+13\hat{j}}{3}$
• C. $\frac{10\hat{i}+13\hat{j}}{3}$
• D. $\frac{-10\hat{i}-13\hat{j}}{3}$

Answer 1

The correct option is A $\frac{10\hat{i}-13\hat{j}}{3}$

We know that the centroid divides the distance between the orthocenter and circumcentre in the ratio 2:1.
$\therefore Centroid=\frac{2\overline{C}+\overline{H}}{3}=\frac{2(4\hat{i}+5\hat{k})+2\hat{i}+3\hat{j}}{3}=\frac{10\hat{i}+13\hat{j}}{3}$
Therefore correct option is a.