Centroid of the tetrahedron OABC, where A ≡ (a, 2, 3) , B ≡ (1, b, 2) , C ≡ (2, 1, c) and O is the origin is (1, 2, 3). The value of a2 + b2 + c2 is equal to :
Answer & explanation
Correct answer: option 1
We have
4 = a + 1 + 2 + 0,
⇒ a = 1,
8 = 2 + b + 1 + 0
⇒ b = 5,
12 = 3 + 2 + c + 0
⇒ c = 7,
∴ a2 + b2 + c2 = 1 + 25 + 49 = 75