Multiple choice

Statement-I: The coordinates of a point equidistant from the four points $(a, 0, 0)$, $(0, b, 0), (0, 0, c), (0, 0, 0)$ are $\left(\dfrac{a}{4}, \dfrac{b}{4}, \dfrac{c}{4}\right)$. Statement-II: The distance between the origin and the centroid of the tetrahedron where vertices are $(0, 0, 0)$, $(a, 0, 0)$, $(0, b, 0)$, $(0, 0, c)$ is $\dfrac{\sqrt{a^2+b^2+c^2}}{4}$. Which of the given statements is correct?

  1. Only I

  2. Only II

  3. Both I and II

  4. Neither I nor II

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A Correct answer