Question:
The planes: $2 x-y+4 z=5$ and $5 x-2.5 y+10 z=6$ are
(A) Perpendicular
(B) Parallel
(C) intersect $y$-axis
(C) passes through $\left(0,0, \frac{5}{4}\right)$
Solution:
The equations of the planes are
$2 x-y+4 z=5$ (1)
$5 x-2.5 y+10 z=6$ (2)
It can be seen that,
$\frac{a_{1}}{a_{2}}=\frac{2}{5}$
$\frac{b_{1}}{b_{2}}=\frac{-1}{-2.5}=\frac{2}{5}$
$\frac{c_{1}}{c_{2}}=\frac{4}{10}=\frac{2}{5}$
$\therefore \frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
Therefore, the given planes are parallel.
Hence, the correct answer is B.