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Suppose the vector equation of a line parallel to the X-axis is

x = 1 + t
y = 2
z = 3

How do I rewrite this into a cartesian equation like the below example?

ƛ = x + 1 = 1 - y = z - 1
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  • $\begingroup$ Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please edit the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. $\endgroup$ Aug 28, 2021 at 1:40
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    $\begingroup$ You cannot express a line in 3d space as a cartesian equation. $\endgroup$ Aug 28, 2021 at 1:54

1 Answer 1

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A line in 3-D space cannot be expressed as a cartesian equation the way it could be expressed in 2-D space.

Take for example 1-D space. Suppose we have $x=1$. We just have one point, $(1)$. Next, go into 2-D space, and $x=1$ is a vertical line, and no longer a point (since any $y$-value will satisfy $x=1$. Then, move into 3-D space, where $x=1$ is a plane, since any $z,y$-values will satisfy $x=1$.

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