Find the Parametric and Cartesian equations of line which passes through the points \(A(-2\mathbf{i}

Question

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 $(2\mathbf{i} + 3\mathbf{j} - 4\mathbf{k})$.

Accepted 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: $\frac{x+2}{-9}=\frac{y-1}{2}=\frac{3-z}{3}$.

Vectors - Equations of Lines

Vectors - Equations of Lines

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