Find the distance between the parallel planes `x+y-z+4=0a n dx+y-z+5=0.`

Explanation

Let `P(x_{1}, y_{1}, z_{1})` be any point on `x+y-z+4=0`. Then,


`x_{1}+y_{1}-z_{1}+4=0`


Let `d` be the distance between the given planes. Then,

`d=` Length of the perpendicular from `P(x_{1}, y_{1}, z_{1})` to `x+y-z+5=0`.


`d=|frac{5-4}{sqrt{1^{2}+1^{2}+(-1)^{2}}}|=frac{1}{sqrt{3}}`
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