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Given the equation: y + z = 10

  • Can it be considered a plane? Why (not)?
  • How do you correctly express planes which are normal onto one axis, for example a plane that lies completely vertical in space or a plane that lies completely horizontal in space?
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    In the $yz$-plane, $y+z=10$ is the equation of a line. In $xyz$-space, it's the equation of a plane. In a $4$-dimensional space, it's the equation of a $3$-dimensional affine subspace. And so on.....2012-04-26
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    Yes, it is the equation for a plane because it is the same as $0x+1y+1z=10$.2012-04-26
  • 0
    A plane that intersects the $x,y,z$-axes at $(a,0,0),(0,b,0),(0,0,c)$ is given by the equation $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$. Since the equation $y+z=10$ is equivalent to $0x+\frac{y}{10}+\frac{z}{10}=1$, we can say that the point $(a,0,0)$ lies at infinity, i.e. the plane is parallel to the $x$-axis.2012-04-26

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