11. Vector a,b,c are coplannar then the value of [a+2b b+2c c+2a] is?

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∣ ∣ ∣ ∣ \begin{matrix} a - b - c & 2 a & 2 a 2 b & b - c - a & 2 b 2 c & 2 c & c - a - b \end{matrix} ∣ ∣ ∣ ∣

\to a, \to b, \to c

{∣ ∣ ∣ 2 \to a - 3 \to b ∣ ∣ ∣}^{2} + {∣ ∣ ∣ 2 \to b - 3 \to c ∣ ∣ ∣}^{2} + {∣ ∣ 2 \to c - 3 \to a ∣ ∣}^{2}

∣ ∣ ∣ ∣ \begin{matrix} a - b - c & 2 a & 2 a 2 b & b - c - a & 2 b 2 c & 2 c & c - a - b \end{matrix} ∣ ∣ ∣ ∣

a, b

c

\frac{2 a}{b + c - a} + \frac{2 b}{c + a - b} + \frac{2 c}{a + b - c}

¯ ¯ ¯ a, ¯ ¯ b, ¯ ¯ c

3 ¯ ¯ ¯ a - 2 ¯ ¯ b - 4 ¯ ¯ c

- ¯ ¯ ¯ a + 2 ¯ ¯ c

- 2 ¯ ¯ ¯ a + ¯ ¯ b + 3 ¯ ¯ c

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