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# Choose the correct answer. The planes: 2x – y + 4z = 5 and 5x – 2.5y + 10z = 6 are:

$\begin{array} ((A)\, Perpendicular \qquad& (B)\, Parallel \\[0.5em] (C)\,intersect \;on\: y-axis\qquad& (D)\,passes \:through\: the \:point\: (0,0,\frac{5}{4}) \end{array}$

Toolbox:
• For the given planes $a_1x+b_1y+c_1z+d_1=0$ and $a_2x+b_2y+c_2z+d_2=0$ if $\large\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ then the planes are parallel.
The given planes are $2x-y+4z=5$
$5x-2.5 y +10z=6$
Let us compare the coefficient of both the planes
$(ie)\;\large\frac{2}{5}=\frac{-1}{-2.5}=\frac{4}{10}$
The ratio is $\large\frac{1}{2.5}$
If $\large\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$ in the two planes
$a_1x +b_1y+c_1z=d_1$
$a_2x +b_2y+c_2z=d_2$
Then the planes are parallel.
Since this condition is satisfied.
Therefore the given planes are parallel.
Therefore option $B$ is correct answer