- #1
roam
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This is a very simple problem but I'm confused because the book's answer is completely different from mine;
Find the parametric vector equation of the plane that passes through the points P(3,1,2), Q(1,3,2) and R(1,1,1).
My attempt at a solution
This is simple, the parametric equations has to be: OX = OP + λPQ + μPR, λ,μ [tex]\in[/tex] R
[tex]\left(\begin{array}{ccc}3\\1\\2\end{ar ray}\right)[/tex] + [tex]\lambda[/tex] [tex] \left(\begin{array}{ccc}-2\\2\\0\end{ar ray}\right)[/tex] + [tex]\mu[/tex] [tex]\left(\begin{array}{ccc}-2\\0\\-1\end{ar ray}\right)[/tex]
I'm confident that this is the right answer & here's a diagram of a similar situation.
http://img114.imageshack.us/img114/9168/planezl4.gif
But the correct answer according to the book has to be:
[tex]\lambda[/tex] [tex]\left(\begin{array}{ccc}3\\1\\2\end{ar ray}\right)[/tex] + [tex]\mu[/tex] [tex]\left(\begin{array}{ccc}1\\3\\2\end{ar ray}\right)[/tex] + [tex](1- \lambda -\mu)[/tex] [tex]\left(\begin{array}{ccc}1\\1\\1\end{ar ray}\right)[/tex]
So, what's wrong?
Find the parametric vector equation of the plane that passes through the points P(3,1,2), Q(1,3,2) and R(1,1,1).
My attempt at a solution
This is simple, the parametric equations has to be: OX = OP + λPQ + μPR, λ,μ [tex]\in[/tex] R
[tex]\left(\begin{array}{ccc}3\\1\\2\end{ar ray}\right)[/tex] + [tex]\lambda[/tex] [tex] \left(\begin{array}{ccc}-2\\2\\0\end{ar ray}\right)[/tex] + [tex]\mu[/tex] [tex]\left(\begin{array}{ccc}-2\\0\\-1\end{ar ray}\right)[/tex]
I'm confident that this is the right answer & here's a diagram of a similar situation.
http://img114.imageshack.us/img114/9168/planezl4.gif
But the correct answer according to the book has to be:
[tex]\lambda[/tex] [tex]\left(\begin{array}{ccc}3\\1\\2\end{ar ray}\right)[/tex] + [tex]\mu[/tex] [tex]\left(\begin{array}{ccc}1\\3\\2\end{ar ray}\right)[/tex] + [tex](1- \lambda -\mu)[/tex] [tex]\left(\begin{array}{ccc}1\\1\\1\end{ar ray}\right)[/tex]
So, what's wrong?
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