Sudden Strike Resource War Free [WORK] Download Full Version
Sudden Strike Resource War Free [WORK] Download Full Version
Sudden Strike Resource War Free Download Full Version
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You can play this game for free right away for as long as you like. Resource War is the first add-on for Sudden Strike 2. The expansion adds a.Q:
A hyperplane of $\mathbb{R}^3$ given by $x_1+2x_2+3x_3=1$
What is the equation of a hyperplane given by the equation $x_1+2x_2+3x_3=1$?
This is just a simple hyperplane in $\mathbb{R}^3$, but I am not sure how to find it.
I am thinking of using the standard definition of a hyperplane in $\mathbb{R}^3$:
A hyperplane in $\mathbb{R}^3$ is the locus of a line whose plane passes through a given point.
I am thinking of using the line
$$\left$$
(the points $(1,2,3)$ and $(1,2,0)$ are in the same line through the origin in $\mathbb{R}^3$, which is the plane given by the equation $x_1+2x_2+3x_3=0$, and this line is parallel to the given hyperplane).
Using this fact and using the plane equation of the given hyperplane, I can now find the equation of the line (by first finding the normal vector to the given hyperplane) and then use linear algebra to find the equation of the given line.
The line would be of the form
$$\alpha \begin{pmatrix}1\\2\\3\end{pmatrix} + \beta \begin{pmatrix}1\\2\\0\end{pmatrix}$$
for some $\alpha,\beta \in \mathbb{R}$.
My question is:
Why is $\beta=0$?
A:
The given hyperplane passes through $(1,1,1)$ because $$(1,1,1)=1\begin{pmatrix}1\\2\\3\end{pmatrix}+2\begin{pmatrix}
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