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Home » Top 10 Battlefield Hardline Tips That Will Obliterate Your Enemy! - Tacotoon

Top 10 Battlefield Hardline Tips That Will Obliterate Your Enemy! - Tacotoon

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 A civil engineer at the World Bank is designing a sustainable pedestrian bridge that follows a linear path defined by the parametric equation \(\mathbf{r}(t) = egin{pmatrix} 1 \ -2 \end{pmatrix} + t egin{pmatrix} 3 \ 1 \end{pmatrix}\). They need to locate the point on this line closest to a proposed water source located at \(egin{pmatrix} 5 \ 4 \end{pmatrix}\). Find the coordinates of this closest point.

📌 The closest point on a line to a given point is the orthogonal projection of that point onto the line.

📌 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 \(\mathbf{d}\):

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