Q. The equation of the line passing through the point of intersection of the lines $x - 3y + 2 = 0$ and $2x + 5y - 7 = 0$ and perpendicular to the line $3x + 2y + 5 = 0$, is
A) $2x - 3y + 1 = 0$
B) $6x - 9y + 11 = 0$
C) $2x - 3y + 5 = 0$
D) $3x - 2y + 1 = 0$
Explanation
(a)
The coordinates of a point of intersection of given lines are (1, 1)
The equation of the perpendicular to the line $3x + 2y + 5 = 0$ is $2x - 3y + \lambda = 0$. It is also passes through (1, 1).
$\therefore\ 2 - 3 + \lambda = 0\ \Rightarrow \ \lambda = 1$
$\therefore$ Required equation of line is $2x - 3y + 1 = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.