If planes x - c y - b z = 0 , c x - y + a z = 0 and b x + a y - z = 0 pass through a straight line then a 2 + b 2 + c 2 =

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Since the given planes pass through a straight line

$\Rightarrow | \begin{matrix} 1 & - c & - b \\ c & - 1 & a \\ b & a & - 1 \end{matrix} | = 0$
$\Rightarrow 1 (1 - a^{2}) + c (- c - a b) - b (a c + b) = 0$
$\Rightarrow 1 - a^{2} - c^{2} - a b c - a b c - b^{2} = 0$
$\Rightarrow 1 - 2 a b c - a^{2} - b^{2} - c^{2} = 0$
$\Rightarrow 1 - 2 a b c = a^{2} + b^{2} + c^{2}$

Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

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