Vectors - Equations of Planes
Vectors - Equations of Planes
A plane \(p\) passes through point \(A\left( 3,2,-5 \right)\). Given that the line \(l:r=\left( \begin{matrix}
1 \\
0 \\
-2 \\
\end{matrix} \right)+\lambda \left( \begin{matrix}
5 \\
2 \\
-2 \\
\end{matrix} \right)\) lies in the plane \(p\). Find the equation of \(p\) in
- parametric form,
- scalar product form,
- Cartesian form.
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Answer:(a) \(\mathbf r=\begin{pmatrix}1\\0\\-2\end{pmatrix}+\lambda\begin{pmatrix}5\\2\\-2\end{pmatrix}+\mu\begin{pmatrix}-2\\-2\\3\end{pmatrix},\ \lambda,\mu\in\mathbb R\) (b) \(\mathbf r\cdot\begin{pmatrix}2\\-11\\-6\end{pmatrix}=14\) (c) \(2x-11y-6z=14\)
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