Evaluating a vector that doesn't belong to a vector combination

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I am solving problems in : Intorduction to Linear Algebra 4th ed.

Problem 23, in Problem set 1 states:

If you look at all combinations of those u, v, and w, is there any vector that can't be produced from eu + dv + ew? Different answer if u, v, ware all in __

given the vectors are:

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I am new to linear Algebra, I don't understand which steps I should go through to evaluate that vector.

In 2D I would say it's a vector that belongs to a perpendicular plane, what is the case here?