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Home » Thus, the area decreases by \(\boxed8\) square centimeters. - Deep Underground Poetry

Thus, the area decreases by \(\boxed8\) square centimeters. - Deep Underground Poetry

📅 May 4, 2026 👤 scraface

May 04, 2026

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\mathbf{v} \cdot \mathbf{c} = (2)(1) + (-1)(2) + (3)(-1) = 2 - 2 - 3 =...
\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:

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