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.
