You are using the word "sum" in a very strange way!

If you are given two lines as

and

then the vector <A, B, C> points in the direction of the first line and the vector <U, V, W> points in the direction of the second line. They are "parallel" if and only if <A, B, C> is a multiple of <U, V, W> and they are not the same line.

To compare L1 with L2, 4= 2(2) but -2 is not 2(1) so they are not parallel nor can they be the same line.

To compare L1 with L3, -8= 4(-2) and 4= 2(-2) but -16 is not 3(-2) so they are not parallel nor can they be the same line.

If that "3" were an "8" so that L1 was given by

then it and L3,

would have parallel vectors.

However, (8, -4, -9) is a point on the first line and putting x= 8, y= -4, z= 9 in the equation of the second,

so these lines would be parallel but NOT equal.