The planes: $2 x - y + 4 z = 5$ and $5 x - 2.5 y + 10 z = 6$ are

Perpendicular

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Parallel

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Co-incident

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None of these

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Solution

The correct option is B Parallel
We have
$2 x - y + 4 z = 5$ and $5 x - 2.5 y + 10 z = 6$

Now,

$\frac{2}{5} = \frac{- 1}{- 2.5} = \frac{4}{10}$

So, the given planes is parallel to each other.

Hence, the option $B$ is the correct answer.

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Similar questions

Q. The planes

2 x - y + 4 z = 5

and

5 x - 2.5 y + 10 z = 6

are

The planes: 2x − y + 4z = 5 and 5x − 2.5y + 10z = 6 are

(A) Perpendicular (B) Parallel (C) intersect y-axis

Q. 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

Choose the correct answer in Question
The planes 2x - y + 4z = 5 and 5x - 2.5y + 10z = 6 are
(a) perpendicular
(b) parallel
(c) intersect along Y-axis
(d) passes through $(0, 0, \frac{5}{4})$

Q. Find the distance between the planes

2 x - y + 2 z = 5

and

5 x - 2.5 y + 5 z = 20

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The planes: 2x−y+4z=5 and 5x−2.5y+10z=6 are

The correct option is B ParallelWe have 2x−y+4z=5 and 5x−2.5y+10z=6Now,25=−1−2.5=410So, the given planes is parallel to each other.Hence, the option B is the correct answer.

The planes: $2 x - y + 4 z = 5$ and $5 x - 2.5 y + 10 z = 6$ are

The correct option is B Parallel
We have
$2 x - y + 4 z = 5$ and $5 x - 2.5 y + 10 z = 6$

Now,

$\frac{2}{5} = \frac{- 1}{- 2.5} = \frac{4}{10}$

So, the given planes is parallel to each other.

Hence, the option $B$ is the correct answer.