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itchy ears on the inside - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \mathbf{c} = \mathbf{i}((-3)(-2) - (1)(4)) - \mathbf{j}((2)(-2) - (1)(1)) + \mathbf{k}((2)(4) - (-3)(1))

📌 = \mathbf{i}(6 - 4) - \mathbf{j}(-4 - 1) + \mathbf{k}(8 + 3)

📌 = \mathbf{i}(2) + \mathbf{j}(5) + \mathbf{k}(11)

📌 = \begin{pmatrix} 2 \\ 5 \\ 11 \end{pmatrix}

📌 Thus, the vector orthogonal to both $\mathbf{a}$ and $\mathbf{b}$ is:

📌 \boxed{\begin{pmatrix} 2 \\ 5 \\ 11 \end{pmatrix}}

📌 An angel investor evaluates a biotech startup's growth vector $\mathbf{g} = \begin{pmatrix} 7 \\ 24 \end{pmatrix}$, seeking a unit vector direction. Find the normalized vector $\mathbf{u}$ in the direction of $\mathbf{g}$.

📌 To find the unit vector $\mathbf{u}$, compute the magnitude of $\mathbf{g}$:

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