Question

If A(1, 3, 2), B(a, b, - 4) and C(5, 1, c) are the vertices of triangle ABC and G(3, b, c) is its centroid, then

पर्याय

• a = `1/2`, b = 1, c = 2

• a = 3, b = - 1, c = `1/3`

• a= 3, b = 2, c = -1

• a = `1/2`, b = 2, c = - 1

Answer 1

a = 3, b = 2, c = -1

Explanation:

G ≡ `((x_1 + x_2 + x_3)/3, (y_1 + y_2 + y_3)/3, (z_1 + z_2 + z_3)/3)`

`=> (3, "b", "c") ≡ (("a + 6")/3, ("b + 4")/3, ("c" - 2)/3)`

`=> 3 = ("a" + 6)/3, "b" = ("b" + 4)/3, "c" = ("c" - 2)/3`

⇒ a = 3, b = 2, c = -1