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Home » Solution: Use Herons formula to compute the area. - All Square Golf

Solution: Use Herons formula to compute the area. - All Square Golf

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 From second equation: \(z = 3x\)

📌 From first: \(3y = 2z = 2(3x) = 6x \Rightarrow y = 2x\)

📌 Substitute into third:

📌 2x - (2x) = 5 \Rightarrow 0 = 5

📌 Contradiction! So no solution exists unless the cross product is orthogonal to \(\mathbf{a}\), which \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix} \cdot egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = 15

📌 e 0\), so inherently inconsistent.

📌 But wait: the cross product must be perpendicular to \(\mathbf{a}\). Check:

📌 egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix} \cdot egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = 15

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