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  • State whether the statements are true or false. The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.

State whether the statements are true or false.

The lines ax + 2y + 1 = 0, bx + 3y + 1 = 0 and cx + 4y + 1 = 0 are concurrent if a, b, c are in G.P.

Answers (1)

Given that ax+2y+1=0    bx+3y+1=0   and cx+4y+1=0  are concurrent .  

  For the lines to be concurrent \begin{vmatrix} a & 2 & 1 \\ b & 3 & 1 \\ c & 4 & 1 \end{vmatrix}=1

 Now expanding along first column we get

 a[3-4]-b[2-4]+c[2-3]=0 

-a+2b-c=0   

2b=a+c  and we know that if a, b ,c are in AP thenb=\frac{a+c}{2} 

 This means given lines are in AP not in GP

Hence, the given statement is False.

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