Perpendicular distance between $2 x + 2 y - z + 1 = 0$ and $2 x + 2 y - x + 4 = 0$ is

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Solution

Perpendicular distance between $2 x + y - z + 1 = 0$

and $2 x + 2 y - z + 4 = 0$ is given by $\frac{| 4 - 1 |}{\sqrt{2^{2} + 2^{2} + (- 1)^{2}}}$

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

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

$= \frac{3}{3}$

$= 1$ .

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