Vectors - Equations of Lines
Vectors - Equations of Lines
Find the Parametric and Cartesian equations of line which passes through the points \(A(-2\mathbf{i} + \mathbf{j} + 3\mathbf{k})\) and perpendicular to both \((\mathbf{i} - 3\mathbf{k})\) and \((2\mathbf{i} + 3\mathbf{j} - 4\mathbf{k})\).
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Answer:Vector equation: \(\mathbf r=\begin{pmatrix}-2 \\ 1 \\ 3\end{pmatrix}+\lambda\begin{pmatrix}-9 \\ 2 \\ -3\end{pmatrix}\). Parametric equations: \(x=-2-9\lambda\), \(y=1+2\lambda\), \(z=3-3\lambda\). Cartesian equation: \(\frac{x+2}{-9}=\frac{y-1}{2}=\frac{3-z}{3}\).
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