Vectors - Equations of Planes
Vectors - Equations of Planes
A plane passes through point \(A(1,0,-2)\), \(B(5,-2,-2)\) and \(C(3,1,-4)\). Find the equation of \(p\) in
- parametric form,
- scalar product form,
- Cartesian form.
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Answer:(a) \(\mathbf r=\begin{pmatrix}1\\0\\-2\end{pmatrix}+\lambda\begin{pmatrix}2\\-1\\0\end{pmatrix}+\mu\begin{pmatrix}2\\1\\-2\end{pmatrix},\ \lambda,\mu\in\mathbb R\) (b) \(\mathbf r\cdot\begin{pmatrix}1\\2\\2\end{pmatrix}=-3\) (c) \(x+2y+2z=-3\)
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