Three Dimensional Geometry Question 12
Question 12 - 2024 (29 Jan Shift 1)
Let $P Q R$ be a triangle with $R(-1,4,2)$. Suppose $M(2,1,2)$ is the mid point of $P Q$. The distance of the centroid of $\triangle PQR$ from the point of intersection of the line $\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}$ and $\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}$ is
(1) 69
(2) 9
(3) $\sqrt{69}$
(4) $\sqrt{99}$
Show Answer
Answer (3)
Solution
Centroid G divides MR in $1: 2$
$G(1,2,2)$
Point of intersection A of given lines is $(2,-6,0)$
$AG=\sqrt{69}$
