The planes:

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.

 

 

 

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