Question

The equation of the straight line perpendicular to the straight line $3x+2y=0$ and passing through the point of intersection of the lines $x+3y-1=0$ and $x-$ $2y+4=0$ is

• A. $2x-3y+1=0$
• B. $2x-3y+3=0$
• C. $2x-3y+5=0$
• D. $2x-3y+7=0$

Answer 1

The correct option is D $2x-3y+7=0$

Given Lines

$x+3y-1=0$---(1)

$x-2y+4=0$---(2)

On solving eq (1) and (2) we get

$5y=5\Rightarrow y=1$

$x+3-1=0\Rightarrow x=-2$

Intersection point of line eq (1) and (2) is $(-2,1)$

Equation of line perpendicular to $3x+2y=0$ is

$2x-3y=\lambda$----(3)

Above equation passing through $(-2,1)$

$-4-3=\lambda \Rightarrow \lambda =-7$

From eq (3)

$2x-3y+7=0$