The balanced combustion reaction of glucose is:
\[\text{C}_6\text{H}_{12}\text{O}_6 + 6\text{O}_2 \rightarrow 6\text{CO}_2 + 6\text{H}_2\text{O}.\]
From the equation:
1 mol of glucose requires 6 mol of $\text{O}_2$.
Molar mass of glucose = $180 \, \text{g/mol}$.
Molar mass of $\text{O}_2 = 32 \, \text{g/mol}$.
Number of moles of glucose in $900 \, \text{g}$:
\[n = \frac{900}{180} = 5 \, \text{mol}.\]
Oxygen required:
\[\text{Mass of } \text{O}_2 = 5 \cdot 6 \cdot 32 = 960 \, \text{g}.\]
Final Answer:
$960 \, \text{g}$.
Let a line passing through the point $ (4,1,0) $ intersect the line $ L_1: \frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4} $ at the point $ A(\alpha, \beta, \gamma) $ and the line $ L_2: x - 6 = y = -z + 4 $ at the point $ B(a, b, c) $. Then $ \begin{vmatrix} 1 & 0 & 1 \\ \alpha & \beta & \gamma \\ a & b & c \end{vmatrix} \text{ is equal to} $