\|\mathbf{g}\| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25
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- \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 $\mathbf{g}$:
- 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}
- Thus, the normalized vector is:
