If ax21+by21+cz21=ax22+by22+cz22=ax23+by23+cz23=d andax2x3+by2y3+cz2z3=ax3x1+by3y1+cz3z1=ax1x2+by1y2+cz1z2=f, where a,b,c,d,f>0 and d>2f, then the value of ∣∣∣∣x1y1z1x2y2z2x3y3z3∣∣∣∣ is:

If ax21+by21+cz21=ax22+by22+cz22=ax23+by23+cz23=d andax2x3+by2y3+cz2z3

1.	If ax21+by21+cz21=ax22+by22+cz22=ax23+by23+cz23=d andax2x3+by2y3+cz2z3=ax3x1+by3y1+cz3z1=ax1x2+by1y2+cz1z2=f, where a,b,c,d,f>0 and d>2f, then the value of ∣∣∣∣x1y1z1x2y2z2x3y3z3∣∣∣∣ is:
Answer» If $a x_{1}^{2} + b y_{1}^{2} + c z_{1}^{2} = a x_{2}^{2} + b y_{2}^{2} + c z_{2}^{2} = a x_{3}^{2} + b y_{3}^{2} + c z_{3}^{2} = d$ and $a x_{2} x_{3} + b y_{2} y_{3} + c z_{2} z_{3} = a x_{3} x_{1} + b y_{3} y_{1} + c z_{3} z_{1} = a x_{1} x_{2} + b y_{1} y_{2} + c z_{1} z_{2} = f,$ where $a, b, c, d, f > 0$ and $d > 2 f,$ then the value of $∣ ∣∣ ∣ \begin{matrix} x_{1} & y_{1} & z_{1} x_{2} & y_{2} & z_{2} x_{3} & y_{3} & z_{3} \end{matrix} ∣ ∣∣ ∣$ is: