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