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Home » From Tiny Bug Egg to Blooming Garden: Watch Seeds Sparkmagic in Just Days! - Londonproperty

From Tiny Bug Egg to Blooming Garden: Watch Seeds Sparkmagic in Just Days! - Londonproperty

📅 March 13, 2026 👤 scraface

Mar 13, 2026

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📌 A civil engineer analyzing directional stability in solar panel arrays needs to find a vector \(\mathbf{v}\) such that \(\mathbf{v} imes egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix} = egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\), where the cross product is defined in 3D. Find a suitable \(\mathbf{v}\).

📌 Let \(\mathbf{v} = egin{pmatrix} x \ y \ z \end{pmatrix}\), \(\mathbf{a} = egin{pmatrix} 1 \ 2 \ 3 \end{pmatrix}\), and \(\mathbf{v} imes \mathbf{a} = egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\).

📌 \mathbf{v} imes \mathbf{a} = egin{vmatrix}

📌 \end{vmatrix} = \mathbf{i}(y \cdot 3 - z \cdot 2) - \mathbf{j}(x \cdot 3 - z \cdot 1) + \mathbf{k}(x \cdot 2 - y \cdot 1)

📌 = egin{pmatrix} 3y - 2z \ - (3x - z) \ 2x - y \end{pmatrix} = egin{pmatrix} 3y - 2z \ -3x + z \ 2x - y \end{pmatrix}

📌 Set equal to \(egin{pmatrix} 0 \ 0 \ 5 \end{pmatrix}\):

📌 3y - 2z = 0 \

📌 -3x + z = 0 \

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