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.
• B.
• C.
• D.

Answer 1

The correct option is A

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.