# 23.   The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are              (A) Perpendicular          (B) Parallel      (C) intersect y-axis      (D) passes through $\left ( 0,0\frac{5}{4} \right )$

Given equations of planes are
$2x-y+4z=5 \ \ \ \ \ \ \ \ \ -(i)$
and
$5x-2.5y+10z=6\\ 2.5(2x-y+4z)=6\\ 2x-y+4z= 2.4 \ \ \ \ \ \ \ \ \ -(ii)$
Now, from equation (i) and (ii) it is clear that given planes are parallel to each other
$\because \frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}\Rightarrow \frac{2}{2}= \frac{-1}{-1}=\frac{4}{4}\Rightarrow 1=1=1$
Therefore, the correct answer is (B)

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