Vectors - Equations of Lines
Vectors - Equations of Lines
Find the Parametric and Cartesian equations of line which passes through the points \(A\left( \begin{matrix}-3\\4 \\5 \end{matrix} \right)\) and \(B\left( \begin{matrix}1\\0\\-3\end{matrix} \right)\).
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Answer:Vector equation: \(\mathbf r=\begin{pmatrix}1 \\ 0 \\ -3\end{pmatrix}+\lambda\begin{pmatrix}1 \\ -1 \\ -2\end{pmatrix}\). Parametric equations: \(x=1+\lambda\), \(y=-\lambda\), \(z=-3-2\lambda\). Cartesian equation: \(x-1=-y=-\frac{z+3}{2}\).
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