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racr^5 - 1r - 1 > 100 - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 A point on the line: \(\mathbf{r}_0 = egin{pmatrix} 1 \ -2 \end{pmatrix}\)

📌 Direction vector: \(\mathbf{d} = egin{pmatrix} 3 \ 1 \end{pmatrix}\)

📌 Point to project: \(\mathbf{p} = egin{pmatrix} 5 \ 4 \end{pmatrix}\)

📌 Vector from point on line to \(\mathbf{p}\):

📌 \mathbf{v} = \mathbf{p} - \mathbf{r}_0 = egin{pmatrix} 5 - 1 \ 4 - (-2) \end{pmatrix} = egin{pmatrix} 4 \ 6 \end{pmatrix}

📌 Project \(\mathbf{v}\) onto \(\mathbf{d}\):

📌 ext{proj}_{\mathbf{d}} \mathbf{v} = \left( rac{\mathbf{v} \cdot \mathbf{d}}{\mathbf{d} \cdot \mathbf{d}}

📌 ight) \mathbf{d}

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