A line passing through the origin perpendicularly cuts the line 3x - 2y = 6 at point M. Find M?

Slope of line 3x - 2y = 6 = $$-\frac{3}{-2} = \frac{3}{2}$$

Product of slopes of two perpendicular lines = -1

Let slope of line passing through origin = $$m$$

=> $$m \times \frac{3}{2} = -1$$

=> $$m = \frac{-2}{3}$$

Equation of line passing through origin and having slope m is $$y = mx$$    (Since y intercept is zero)

=> $$y = \frac{-2}{3} x$$

=> $$3y = -2x$$ => $$2x + 3y = 0$$ 

Solving the above equations, we get the intersection point M = $$(\frac{18}{13} , \frac{-12}{13})$$

=> Ans - (B)