Using the property of determinants and without expanding, prove that: \(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}=0\)
\(\begin{vmatrix}x&a&x+a\\y&b&y+b\\z&C&z+c\end{vmatrix}\)
=\(\begin{vmatrix}x&a&x\\y&b&y\\z&c&z\end{vmatrix}+\begin{vmatrix}x&a&a\\y&b&b\\z&c&c\end{vmatrix}=0+0=0\)
[Here the two columns of the determinants are identical]
A settling chamber is used for the removal of discrete particulate matter from air with the following conditions. Horizontal velocity of air = 0.2 m/s; Temperature of air stream = 77°C; Specific gravity of particle to be removed = 2.65; Chamber length = 12 m; Chamber height = 2 m; Viscosity of air at 77°C = 2.1 × 10\(^{-5}\) kg/m·s; Acceleration due to gravity (g) = 9.81 m/s²; Density of air at 77°C = 1.0 kg/m³; Assume the density of water as 1000 kg/m³ and Laminar condition exists in the chamber.
The minimum size of particle that will be removed with 100% efficiency in the settling chamber (in $\mu$m is .......... (round off to one decimal place).
Read More: Properties of Determinants