You need to identify the direction vectors of the lines such that:

barv_1 = <2,-6,4> , barv_2 = <-1,3,-2> , barv_3 = <1,-3,2>, barv_4 = <2,-3,1>

You need to remember that two vectors are parallel if the coressponding components of both vectors are in the same ratio.

Checking if the vectors `barv_1` and `barv_2` are parallel yields:

`2/(-1) = (-6)/3 = 4/(-2)`

`-2 = -2 = -2`

The same ratio proves that the vectors `barv_1` and `barv_2` are parallel.

Checking if the vectors `barv_1` and `barv_3` are parallel yields:

`2/1 = (-6)/(-3) = 4/2`

`2 = 2 = 2`

The same ratio proves that the vectors `barv_1` and `barv_3 ` are parallel.

Checking if the vectors `barv_1` and `barv_4` are parallel yields:

`2/2 != (-6)/(-3) != 4/1`

The different ratios prove that the vectors `barv_1` and `barv_4` are not parallel.

Checking if the vectors `barv_2` and `barv_3` are parallel yields:

`(-1)/1 = 3/(-3) = (-2)/2`

`-1 = -1 = -1`

The same ratio proves that the vectors `barv_2` and `barv_3` are parallel.

Checking if the vectors `barv_2` and `barv_4` are parallel yields:

`(-1)/2 != 3/(-3) != (-2)/1`

The different ratios prove that the vectors `barv_2` and `barv_4` are not parallel.

Checking if the vectors `barv_3` and `barv_4` are parallel yields:

`(1)/2 != (-3)/(-3) != (2)/1`

The different ratios prove that the vectors `barv_3` and `barv_4` are not parallel.

**Hence, the line given at the point d) , `bar r = (3,-5,-3) + s(2,-3,1)` is not parallel to the other three lines.**

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