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victus00 [196]
2 years ago
7

Describe the surface in double-struck r3 represented by the equation x + y = 3. this is the set {(x, y, 3 − x − y)|x is in doubl

e-struck r, y is in double-struck r} which is a vertical plane that intersects the xy-plane in the line y = 3 − x, z = 0.

Mathematics
1 answer:
sashaice [31]2 years ago
3 0
First, note that <span>x+y=3</span><span> is a linear in </span>x<span> and </span>y<span>, and independent of </span>z<span>. So, this is just a line in the </span><span>xy</span>-plane, extended into and out of the plane. Since we have the line, we have all the points we need;  <span>

</span>the equation in R3 is a plane<span> parallel to the z-axis and contains the line
y = 3 - x </span> 
The plan sketched below.

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