$∣ ∣ ∣ ∣ ∣ \begin{matrix} l^{2} - m^{2} & a - b & x^{3} - y^{3} m^{2} - n^{2} & b - c & y^{3} - z^{3} n^{2} - l^{2} & c - a & z^{3} - x^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣$ =........

\sum l^{2} b z^{3}

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- \sum l^{2} b z^{3}

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\sum m^{2} c x^{3}

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Solution

The correct option is D 0
Performing $R_{1} \to R_{1} + R_{2} + R_{3}$ , the given determinant transforms to

$∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & 0 & 0 m^{2} - n^{2} & b - c & y^{3} - z^{3} n^{2} - l^{2} & c - a & z^{3} - r^{3} \end{matrix} ∣ ∣ ∣ ∣ ∣ = 0$

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Similar questions

a^{3} (b z - c y)^{3} + b^{3} (c x - a z)^{3} + c^{3} (a y - b x)^{3} = 3 a b c (b z - c y) (c x - a z) (a y - b x)

l_{1} parallel to l_{2}

l_{1} perpendicular to l_{2}

The representation of $l_{1} parallel to l_{2}$ and $l_{3} perpendicular to l_{2}$ is respectively,

A X_{3}, B X_{3}

C Y_{3}

4.97 \times 10^{- 30}, 0.60 \times 10^{- 30}

0.00

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