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Homogeneous System of Equations

If the planes...

Question

If the planes x = cy + bz, y = az + cx and z = bx + ay passing through a line, then $a^{2} + b^{2} + c^{2} + 2 a b c$ =

A

-1

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B

1

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C

2

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Solution

The correct option is B 1
The given equation has infinite number of solution.
$\Rightarrow ∣ ∣ ∣ ∣ \begin{matrix} 1 & - c & - b - c & 1 & - a - b & - a & 1 \end{matrix} ∣ ∣ ∣ ∣ = 0 \Rightarrow a^{2} + b^{2} + c^{2} + 2 a b c = 1$

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