Question

find the equation of line passing through( 1,-2,3)and parallel to 3x+z-2=0 and x-2y+z+5=0

Answer 1

If the line is parallel to both planes, it must be perpendicular to both their normals.

You have the direction numbers of the normals, and their cross product is perpendicular to both of them.

That will give you the direction numbers of the desired line, which you can then express in the usual way, given a point on the line.