If -1 - a12-b1-c1 a1a2-b2-c2 a1a3-b3-c3 b1b2-c1 b22-c2 b2b3-c3 c3c1 c3c2 c32 and -2 - a1 b1 c1 a2 b2 c2 a3 b3 c3 - then - 1- 2 is equal to

The correct option is A a_1b_2c_3 Δ_1 = nbsp;a_1^2+b_1+c_1 amp; a_1a_2+b_2+c_2 amp;a_1a_3+b_3+c_3 nbsp; nbsp;b_1b_2+c_1 amp; b_2 ...

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Properties of Determinants

If Δ1 = a...

Question

If $Δ_{1}$ = $∣ ∣ ∣ ∣ ∣ \begin{matrix} a_{1}^{2} + b_{1} + c_{1} & a_{1} a_{2} + b_{2} + c_{2} & a_{1} a_{3} + b_{3} + c_{3} b_{1} b_{2} + c_{1} & b_{2}^{2} + c_{2} & b_{2} b_{3} + c_{3} c_{3} c_{1} & c_{3} c_{2} & c_{3}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣$ and $Δ_{2}$ = $∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣$ , then $\frac{Δ_{1}}{Δ_{2}}$ is equal to

a_{1} b_{2} c_{3}

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a_{1} a_{2} a_{3}

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a_{3} b_{2} c_{1}

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a_{1} b_{1} c_{1} + a_{2} b_{2} c_{2} + a_{3} b_{3} c_{3}

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△_{1} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} a_{1}^{2} + b_{1} + c_{1} & a_{1} a_{2} + b_{2} + c_{2} & a_{1} a_{3} + b_{3} + c_{3} b_{1} b_{2} + c_{1} & b_{2}^{2} + c_{2} & b_{2} b_{3} + c_{3} c_{3} c_{1} & c_{3} c_{2} & c_{3}^{2} \end{matrix} ∣ ∣ ∣ ∣ ∣

△_{2} = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

\frac{△_{1}}{△_{2}}

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} a_{1} & b_{1} & c_{1} a_{2} & b_{2} & c_{2} a_{3} & b_{3} & c_{3} \end{matrix} ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} α_{1} & β_{1} & γ_{1} α_{2} & β_{2} & γ_{2} α_{3} & β_{3} & γ_{3} \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ_{1} \times Δ_{2}

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} a & b & c x & y & z p & q & r \end{matrix} ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} y & b & q x & a & p z & c & r \end{matrix} ∣ ∣ ∣ ∣

Δ_{1}

Δ_{1} = ∣ ∣ ∣ ∣ \begin{matrix} 7 & x & 2 - 5 & x + 1 & 3 4 & x & 7 \end{matrix} ∣ ∣ ∣ ∣, Δ_{2} = ∣ ∣ ∣ ∣ \begin{matrix} x & 2 & 7 x + 1 & 3 & - 5 x & 7 & 4 \end{matrix} ∣ ∣ ∣ ∣

Δ_{1} - Δ_{2} = 0

Δ_{1} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & cos α & cos β cos α & 1 & cos γ cos β & cos γ & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ_{2} = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 0 & cos α & cos β cos α & 0 & cos γ cos β & cos γ & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣

Δ_{1} = Δ_{2}

{sin}^{2} α + {sin}^{2} β + {sin}^{2} γ

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