Question

Find the distance between the given parallel planes. 4x − 5y z = 16, 8x − 10y 2z = 2

Answer 1

The distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.

What is a plane?

A plane is a flat surface on which a straight line joining any two points on it would wholly lie.

Given equations are

$4x-5y+z=16$

$8x-10y+2z=2$

The distance between two planes is given by the formula:

$D=\dfrac{|d_2-d_1|}{\sqrt{a^2+b^2+c^2}}$

Here from equations  

$4x-5y+z=16$

$8x-10y+2z=2$

We can also write the equation  $8x-10y+2z=2$  as:

$4x-5y+z=1$

So now the two equations are:

$4x-5y+z=16$

$4x-5y+z=1$

here a=4  b=-5  c =1 and d1=16  d2=1

Putting the values in the equation.

$D=\dfrac{|-16+1|}{\sqrt{4^2+(-5)^2+(10^2)}}$

$D=2.34$

Hence the distance between the two planes 4x-5y+z=16 and 8x-10y+2z=2 will be 2.34 units.

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