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Home » y = (-1 + \sqrt7) + 2 = 1 + \sqrt7, \quad y = (-1 - \sqrt7) + 2 = 1 - \sqrt7 - Crosslake

y = (-1 + \sqrt7) + 2 = 1 + \sqrt7, \quad y = (-1 - \sqrt7) + 2 = 1 - \sqrt7 - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 = \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 $\mathbf{g}$:

📌 \|\mathbf{g}\| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25

📌 The unit vector is:

📌 \mathbf{u} = \frac{1}{\|\mathbf{g}\|} \mathbf{g} = \frac{1}{25} \begin{pmatrix} 7 \\ 24 \end{pmatrix} = \begin{pmatrix} \frac{7}{25} \\ \frac{24}{25} \end{pmatrix}

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