Find the condition for two straight lines to be perpendicular

1.	Find the condition for two straight lines to be perpendicular
Answer» let slope of lines l₁ and l₂ are respectively m₁ and m₂. we know that the the angle between two lines whose slopes are m₁ & m₂ is given by tanθ = \(\frac{m_1\,-\,m_2}{1\,+\,m_1\,m_2},\).....(1) where θ is angle between lines l₁ and l₂. for lines l₁ & l₂ to be perpendicular, we have θ = 90° \(\Rightarrow\) tanθ = tan90° = ∞ = \(\frac{1}{0}\) therefore, equation (i), we have \(\frac{m_1\,-\,m_2}{1\,+\,m_1\,m_2}=\frac{1}{0}\) \(\Rightarrow\) 1 + m₁ m₂ = 0 \(\Rightarrow\) m₁ m₂ = -1. Hence, two straight line are perpendiculer is the product of there slopes is equal to -1.

Answer»

let slope of lines l₁ and l₂ are respectively m₁ and m₂.

we know that the the angle between two lines whose slopes are m₁ & m₂ is given by

tanθ = \(\frac{m_1\,-\,m_2}{1\,+\,m_1\,m_2},\).....(1)

where θ is angle between lines l₁ and l₂.

for lines l₁ & l₂ to be perpendicular,

we have θ = 90°

\(\Rightarrow\) tanθ = tan90° = ∞ = \(\frac{1}{0}\)

therefore, equation (i), we have

\(\frac{m_1\,-\,m_2}{1\,+\,m_1\,m_2}=\frac{1}{0}\)

\(\Rightarrow\) 1 + m₁ m₂ = 0

\(\Rightarrow\) m₁ m₂ = -1.

Hence, two straight line are perpendiculer is the product of there slopes is equal to -1.

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