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Kalij13

03.05.2021

Mathematics

$\textbf{The distance between $l_1$ \& $l_2$ is given by $\frac{3}{\sqrt{2}}$}\\$

Step-by-step explanation: $\textup{Given:}\\$y = x + 3$ \hspace{5mm} \& \hspace{5mm} $-x + y = 0$\\\textup{When the lines are of the form:}\\ $ ax + by = c_1 $\\$ ax + by = c_2 $\\\textup{The distance between these two lines is given by:}\\$$ d = \frac{|c_2 - c_1|}{\sqrt{a^2 + b^2}} $$\\\textup{The given lines can be written in the above form as:}\\$

$\begin{equation}x - y + 3 = 0 \end{equation}\begin{equation}x - y = 0 \end{equation}\\$$\\\textup{Comparing with the standard form, we get}\\$$ d = \frac{|0 - (-3)|}{\sqrt{1^2 + 1^2}} $$\\$$ \therefore d = \frac{3}{\sqrt{2}}$

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