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Understanding the Context

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\boxed{a = 3,\ b = 2,\ c = 0,\ d = 0}
Question:** During a workshop on AI ethics, a facilitator uses a geometric model where two vectors represent conflicting values: \( \vec{v} = \begin{pmatrix} 2 \\ -1 \end{pmatrix} \) and \( \vec{w} = \begin{pmatrix} x \\ 4 \end{pmatrix} \). Find \( x \) such that \( \vec{v} \) and \( \vec{w} \) are perpendicular, illustrating balanced ethical trade-offs.
Two vectors are perpendicular if their dot product is zero.

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