If A-1 1 1a b c a3 b3 c3-B-1 1 1a2 b2 c2a3 b3 c3-C-a b ca2 b2 c2a3 b3 c3- then which relation is correct

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Properties of Determinants

If A=1 1 ...

Question

If $A = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣, B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣, C = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣,$ then which relation is correct

A = B

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A = C

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B = C

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None of these

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A = ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣, B = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣, C = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & b & c a^{2} & b^{2} & c^{2} a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣,

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ = (a - b) (b - c) (c - a) (a + b + c)

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 (x - a)^{2} & (x - b)^{2} & (x - c)^{2} (x - b) (x - c) & (x - c) (x - a) & (x - a) (x - b) \end{matrix} ∣ ∣ ∣ ∣ ∣

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ = (b - c) (c - a) (a - b) (a + b + c)

∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 a & b & c a^{3} & b^{3} & c^{3} \end{matrix} ∣ ∣ ∣ ∣ = (a - b) (b - c) (c - a) (a + b + c)

∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & 1 & 1 (x - a)^{2} & (x - b)^{2} & (x - c)^{2} (x - b) (x - c) & (x - c) (x - a) & (x - a) (x - b) \end{matrix} ∣ ∣ ∣ ∣ ∣

In the adjoining figure, if $B C = a, A C = b, A B = c$ and $∠ C A B = 120^{\circ}$ ,
then which of the following is the correct relation?

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