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Home » Solution: The slope of the terrain is given by the derivative: - Upplift

Solution: The slope of the terrain is given by the derivative: - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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\mathbf{c} \cdot \mathbf{c} = 1^2 + 2^2 + (-1)^2 = 1 + 4 + 1 = 6
ext{proj}_{\mathbf{c}} \mathbf{v} = rac{-3}{6} egin{pmatrix} 1 \ 2 \...
Now compute the perpendicular component:
\mathbf{v}_{\perp} = egin{pmatrix} 2 \ -1 \ 3 \end{pmatrix} - egin{p...
The magnitude of the perpendicular component (which is the desired qua...
\|\mathbf{v}_{\perp}\| = \sqrt{(2.5)^2 + 0^2 + (2.5)^2} = \sqrt{6.25 +...
Alternatively, using formula for perpendicular component magnitude:
\|\mathbf{v}_{\perp}\| = \sqrt{\|\mathbf{v}\|^2 - \left(rac{|\mathbf{...
But since we already computed it:
oxed{\dfrac{5\sqrt{2}}{2}}

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