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Olympic rowers for Poland - Groen Casting

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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Calculate the determinant:
\mathbf{c} = \mathbf{i}((-3)(-2) - (1)(4)) - \mathbf{j}((2)(-2) - (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...
To find the unit vector $\mathbf{u}$, compute the magnitude of $\mathb...
\|\mathbf{g}\| = \sqrt{7^2 + 24^2} = \sqrt{49 + 576} = \sqrt{625} = 25

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\mathbf{u} \cdot \mathbf{v} = 1,\quad \mathbf{v} \cdot \mathbf{w} = 6.
Assume all vectors lie in a 3D subspace. Express \(\mathbf{u}\) and \(...
Let us apply the inequality:
but refine using vector decomposition. Decompose \(\mathbf{w}\) into c...
\mathbf{w} = \mathbf{w}_\parallel + \mathbf{w}_\perp, \quad \mathbf{w}...
\|\mathbf{w}_\perp\|^2 = \|\mathbf{w}\|^2 - \|\mathbf{w}_\parallel\|^2...
Now, \(\mathbf{u} \cdot \mathbf{w} = \mathbf{u} \cdot \mathbf{w}_\para...
Since \(\|\mathbf{u} - \mathbf{u} \cdot \mathbf{v} \mathbf{v}\| \geq 0...
\|\mathbf{u}_\perp\|^2 = \|\mathbf{u}\|^2 - (\mathbf{u} \cdot \mathbf{...
Let \(\mathbf{u}_\perp = \mathbf{u} - \frac{1}{9} \mathbf{v}\) (since...

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