The lines 2x=3y=-z and 6x=-y=-4z

are perpendicular
intersect at an angle 45 degree
are parallel
intersect at an angle 60 degree

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Letting $z=6$ for the first line and $y=12$ for the second, we find the direction vectors $(-3,-2,6)$ and $(-2,12,3)$ , resp. The lines are perpendicular as the dot product of these two vectors is 0; the two lines intersect at the origin.