10. vector algebra — ગણિત ધોરણ 12 સાયન્સ — Question

$[\overline{ AB } \overline{ AC } \overline{ AD }]=0$

$\left|\begin{array}{ccc}3 & -1 & -8 \\ -1 & \lambda-3 & -1 \\ \lambda-2 & -1 & -6\end{array}\right|=0$

$\Rightarrow[-6(\lambda-3)-1]-8(1-(\lambda-3)(\lambda-2))+(6+(\lambda$

$-2)=0$

$3(-6 \lambda+17)-8\left(-\lambda^{2}+5 \lambda-5\right)+(\lambda+4)=8$

$8 \lambda^{2}-57 \lambda+95=0$

$\lambda_{1} \lambda_{2}=\frac{95}{8}$