If a, b and c are unit vectors, then $| a - b |^{2} + | b - c |^{2} + | c - a |^{2}$ does not exceed

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B 9
$| a - b |^{2} + | b - c |^{2} + | c - a |^{2} = 2 (a^{2} + b^{2} + c^{2}) - 2 (a . b + b . c + c . a) = 2 \times 3 - 2 (a . b + b . c + c . a) = 6 - (a + b + c)^{2} + a^{2} + b^{2} + c^{2} = 9 - | a + b + c |^{2} \leq 9$ .

Suggest Corrections

Similar questions

| a - b |^{2} + | b - c |^{2} + | c - a |^{2}

a, b

c

{| a - b |}^{2} + {| b - c |}^{2} + {| c - a |}^{2}

\to a, \to b, \to c

{∣ ∣ ∣ \to a - \to b ∣ ∣ ∣}^{2} + {∣ ∣ ∣ \to b - \to c ∣ ∣ ∣}^{2} + {∣ ∣ \to c - \to a ∣ ∣}^{2}

¯ ¯ ¯ a . ¯ ¯ b, ¯ ¯ c

| ¯ ¯ ¯ a - ¯ ¯ b |^{2} + | ¯ ¯ b - ¯ ¯ c |^{2} + | ¯ ¯ c - ¯ ¯ ¯ a |^{2}

| a - b |^{2} + | b - c |^{2} + | c - a |^{2}

Join BYJU'S Learning Program