Assertion (A): If (-1,3,2) and (5,3,2) are re | vedclass

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(C) In any triangle, the centroid divides the line segment joining the orthocentre and the circumcentre in the ratio $2: 1$.Let the orthocentre be $O(

Vedclass · Accepted Answer

$A$ is true, $R$ is false

Vedclass · Answer

(C) In any triangle, the centroid divides the line segment joining the orthocentre and the circumcentre in the ratio $2: 1$.Let the orthocentre be $O(-1, 3, 2)$ and the circumcentre be $C(5, 3, 2)$.The centroid $G$ divides the line segment $OC$ in the ratio $2: 1$.Using the section formula, the coordinates of $G$ are:$G = \left( \frac{2(5) + 1(-1)}{2+1}, \frac{2(3) + 1(3)}{2+1}, \frac{2(2) + 1(2)}{2+1} \right)$$G = \left( \frac{10-1}{3}, \frac{6+3}{3}, \frac{4+2}{3} \right)$$G = \left( \frac{9}{3}, \frac{9}{3}, \frac{6}{3} \right) = (3, 3, 2)$.Thus, Assertion $(A)$ is true.Reason $(R)$ states that the ratio is $1: 2$, which is incorrect because the correct ratio is $2: 1$.Therefore, $(A)$ is true and $(R)$ is false.

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