Can't find a second direction vector needed to solve. Help please.

Find a vector equation of the line passing through P(1,1,2), intersecting the line [2 1 0] + t[1 1 1], and perpendicular to that line.

The answer key says the solution is [1 1 2] + t[4 1 -5], which means the second direction vector I'm looking for is [-5 0 -4] so I can pair with with [1 1 1] and derive a normal of [4 1 -5] through the cross-product. The problem is I have no idea how to get to a direction vector of [-5 0 -4] given the information. I know it has something to do with the lines intersecting and being perpendicular, but I don't know how to put it all together. Any help would be appreciated.