Given: The coordinates of the A, B and C of the triangle ABC are (a, 1, 3), (-2, b, -5) and (4, 7, c) respectively. The centroid of the triangle is (0, 0, 0)

To find: the values of a, b, c

Formula used:

Centroid of triangle ABC whose vertices are A(x₁, y₁, z₁), B(x₂, y₂, z₂) and C(x₃, y₃, z₃) is given by,

Here A(a, 1, 3), B(-2, b, -5) and C(4, 7, c)

Centroid of the triangle

On comparing:

⇒ a + 2 = 0

⇒ a = –2

⇒ b + 5 = 0

⇒ b = –5

⇒ c – 2 = 0

⇒ c = 2

Hence, values of a, b and c are -2, -5, 2