Hello, rcmango!

This is quite straight-forward.

Exactlywhereis your difficulty?

Find the symmetric equations of the straight line that passes through the point (1,-2,3)

and is perpendicular to the plane 2x + 3y = 0

We have a point on the line: .(x1, y1, z1) .= .(1,-2,3)

Since the line is perpendicular to the plane,

. . its direction is the normal vector of the plane: .[2,3,0]

Can you write the symmetric equatons now?