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axxon
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parametric and symmetric equations in R^3??
Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R3. Support your answer using examples.
This question had me thinking for a while, but i want to confirm my understanding or if i am even correct.
I think the line is perpendicular to the Z-axis, So does this mean that the directional vector for z component is 0? basically [ax,ay,0].But couldn't it be perpendicular to xy plane, and still have a directional z component?
But besides that, using that information, in terms of parametric equation it tells us that
the z is just going to equal the position vectors z component.
Now here is where i get confused...with the symmetric equation.
Can you guys please explains this to me in simplest terms...i am trying really hard to understand this vectors in 3 space stuff.
Homework Statement
Recall that there are three coordinates planes in 3-space. A line in R3 is parallel to xy-plane, but not to any of the axes. Explain what this tells you about parametric and symmetric equations in R3. Support your answer using examples.
Homework Equations
The Attempt at a Solution
This question had me thinking for a while, but i want to confirm my understanding or if i am even correct.
I think the line is perpendicular to the Z-axis, So does this mean that the directional vector for z component is 0? basically [ax,ay,0].But couldn't it be perpendicular to xy plane, and still have a directional z component?
But besides that, using that information, in terms of parametric equation it tells us that
the z is just going to equal the position vectors z component.
Now here is where i get confused...with the symmetric equation.
Can you guys please explains this to me in simplest terms...i am trying really hard to understand this vectors in 3 space stuff.
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