The Slope of a line is double of the slope of another line. If tangent of the angle between them is 1/3, find the slopes of the line.

Q.No. 11 of Exercise 10.1 of Class 11th

The angle between x-axis and the line joining the points A(3,-1) and (4,-2).

Sol :

Let m₁ and m_{2 be the slopes of the two lines.}

_{Given that}        m₁ = 2m₂

 
Let x be the angle between the lines.

We know that,         tanx = m₁ – m₂/1+m₁m₂

                

_{Therefore,               1/3   =}   m₁ – m₂/1+m₁m₂

_Putting       m₁ = 2m_2,

_{Therefore,              1/3  =} 2m₂ – m₂/1+2m₂m₂ 

                                 

      _{Or                          1/3   =}   m₂/1+2m₂²

       ^Or                          3m₂  = 1+2m₂²

        Or                2m₂²-3m₂+1 = 0

       Or          2m₂²-2m₂- m₂+1 = 0

      Or        2m₂(m₂-1)-1(m₂-1) = 0

      Or              (2m₂-1)( m₂-1) = 0

Therefore,        m_{2 = 1/2      OR}          m_{2 = 1}   

Now,

         For   m_{2 = 1/2}         m_{1 = 1}

_{and   For}     m_{2 = 1}          m_{1= 2}

_{Hence, Slope of these lines are  1, 1/2 or 2,1.}