Q89 / 150 · MHT CET 2022 (10 Aug Shift 2) · Mathematics

If $A \equiv(5,1, p), B \equiv(1, q, p)$ and $C \equiv(1,-2,3)$ are vertices of the triangle and $G \equiv\left(r,-\frac{4}{3}, \frac{1}{3}\right)$ is its centroid, then the values of $p, q, r$ are respectively

  • A
    $-1,3, \frac{7}{3}$
  • B
    $1,3, \frac{7}{3}$
  • C
    $1,-3, \frac{7}{3}$
  • Correct answer
    D
    $-1,-3, \frac{7}{3}$

Solution

$\begin{aligned} & \left(r, \frac{-4}{3}, \frac{1}{3}\right) \equiv\left(\frac{5+1+1}{3}, \frac{1+q-2}{3}, \frac{p+p+3}{3}\right) \\ & \Rightarrow r=\frac{7}{3}, \frac{-4}{3}=\frac{q-1}{3}, \frac{1}{3}=\frac{2 p+3}{3} \\ & \Rightarrow p=-1, q=-3, r=\frac{7}{3}\end{aligned}$

Hence, the correct answer is option: 'D'.

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