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Home » Who Is the Duchess Behind the Legend of the Unforgettable Night Reign? - SUpost

Who Is the Duchess Behind the Legend of the Unforgettable Night Reign? - SUpost

📅 July 7, 2026 👤 scraface

Jul 07, 2026

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📌 $ q + 3 = -5 \Rightarrow q = -8 $

📌 The sum is $ 2 + (-8) = -6 $.

📌 The final answer is \boxed{-6}.Question: An anthropologist models the migration paths of two ancient tribes as vectors $\vec{u} = \begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix}$ and $\vec{v} = \begin{pmatrix} -2 \\ 4 \\ 1 \end{pmatrix}$. There exists a vector $\vec{w} = \begin{pmatrix} a \\ b \\ c \end{pmatrix}$ such that $\vec{w} = 2\vec{u} - 3\vec{v}$. Find $\vec{w}$.

📌 To find $\vec{w}$, we compute the linear combination:

📌 \vec{w} = 2\vec{u} - 3\vec{v} = 2\begin{pmatrix} 3 \\ -1 \\ 2 \end{pmatrix} - 3\begin{pmatrix} -2 \\ 4 \\ 1 \end{pmatrix}

📌 Distribute the scalars:

📌 \vec{w} = \begin{pmatrix} 2 \cdot 3 \\ 2 \cdot (-1) \\ 2 \cdot 2 \end{pmatrix} - \begin{pmatrix} 3 \cdot (-2) \\ 3 \cdot 4 \\ 3 \cdot 1 \end{pmatrix} = \begin{pmatrix} 6 \\ -2 \\ 4 \end{pmatrix} - \begin{pmatrix} -6 \\ 12 \\ 3 \end{pmatrix}

📌 Subtract the vectors component-wise:

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