How would I calculate a vector X where it "goes" the same directions to 2 positions?

the title may be confusing, but what I want to achieve is to calculate an unknown vector, X. the direction between X and another vector A will be A’s lookvector. the direction between X and another vector B will be B’s lookvector. here’s an image to explain what I mean:
image
as you can see, the direction between vector X and vector A will be the direction vector A is going. same goes for Vector B. i want to find the X vector (the orange).

This is just vector intersection. There are tons of resources online on this.

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