Question

$\huge\mathfrak\purple{♡Question}$

Find the distance between the planes:
2x - y + 2z = 5 and 5x - 2.5y + 5z = 20
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Answer 1

given equation of two planes,

2x - y + 2z = 5

5x - 2.5y + 5z = 20

divide both sides by 2.5 in second equation,

5/2.5x - 2.5y/ 2.5 + 5z/2.5

2x - y + 2z = 8

now, u can see that both planes are parallel.

distance between two parallel planes=

|8-5| /√( 2² + 1² + 2²)

= 3/3= 1 unit

hope it helps..... :)

Answer 2

$\huge\underline{\overline{\mid{\bold{\pink{ᴀɴswᴇʀ}}\mid}}}$

P¹ = 2x - y + 2x = 5

P² = 2x - 2.5y + 5z = 20

=> 2x - y + 2z = 20/2.5

= 20/5 × 2

= 8

Distance = $| \frac{d {}^{2} - d {}^{1} }{ \sqrt{a {}^{2} + b {}^{2} + c {}^{2} } } |$

$= | \frac{8 - 5}{ \sqrt{(2) {}^{2} + ( - 1) {}^{2} + (2) {}^{2} } } |$

$= | \frac{3 }{ \sqrt{4 + 1 + 4} } |$

$= | \frac{3}{ \sqrt{9} } |$

$= \frac{3}{3}$

$= 1 \: unit$

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