Parameterization problem help

  • Thread starter -EquinoX-
  • Start date
In summary, to parameterize the line segment from the point (1,4,-2) to the point (6,7,-2), you can use the vector equation \vec{r}(t)= (6+ 5t)\vec{i}+ (7+ 3t)\vec{j}- 2\vec{k}, where 0=<t=<1.
  • #1
564
1

Homework Statement



Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).

Homework Equations


The Attempt at a Solution



I got:

[tex] \vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k} [/tex]

for some reason webassign tells me it's wrong
 
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  • #2
Hi -EquinoX-! :smile:
-EquinoX- said:
Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).

I got:

[tex] \vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k} [/tex]

erm :redface: … it's minus 2k, isn't it ? :wink:

(and some brackets would be a good idea :rolleyes:)
 
  • #3


tiny-tim said:
Hi -EquinoX-! :smile:


erm :redface: … it's minus 2k, isn't it ? :wink:

(and some brackets would be a good idea :rolleyes:)

yes it's -2k, I just mistyped it.. still gives me the wrong answers
 
  • #4


well, look at it this way.

let r_o=<1,4,-2>, and let u=<5,3,0>. if P1(1,4,-2) and P2(6,7,-2) then as you can see
u=P1P2
Let, r=<x,y,z>

then in general the equation of the line that passes through P1 and whose diercition is along the vector u, is

r=r_o+tu =>

r=i+4j-2k+5ti+3tj=(1+5t)i+(4+3t)j-2k

where 0=<t=<1.
 
  • #5
-EquinoX- said:
… still gives me the wrong answers

In that case, either it doesn't like your absence of brackets, or since it asked for "the line segment from …", it probably expects t to be increasing in that direction. :wink:
 
  • #6


-EquinoX- said:

Homework Statement



Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).


Homework Equations





The Attempt at a Solution



I got:

[tex] \vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k} [/tex]

for some reason webassign tells me it's wrong
that doesn't even make sense. You are adding numbers to vectors. Do you mean
[tex]\vec{r}(t)= (6+ 5t)\vec{i}+ (7+ 3t)\vec{j}- 2\vec{k}[/tex]
 

1. What is the parameterization problem?

The parameterization problem is a common issue in scientific research, particularly in computer simulations and modeling. It refers to the difficulty of accurately representing real-world phenomena using a limited number of variables or parameters. In other words, it is the challenge of finding the best way to describe a complex system with a simplified model.

2. Why is the parameterization problem important?

The accuracy of scientific models and simulations relies heavily on how well the parameterization problem is addressed. If the model is not properly parameterized, the results may be inaccurate and unreliable. This can have serious consequences in fields such as climate change research, where accurate predictions are crucial for decision-making.

3. How do scientists approach the parameterization problem?

There is no one-size-fits-all solution to the parameterization problem, as it varies depending on the specific research question and system being studied. However, scientists typically use a combination of data analysis, theoretical models, and experimental data to identify the most important parameters and determine their values.

4. What are some common challenges in addressing the parameterization problem?

One of the main challenges in addressing the parameterization problem is the trade-off between simplicity and accuracy. A highly complex model may be more accurate, but it may also be more difficult to interpret and apply. Additionally, data limitations and uncertainties in the underlying processes can make it difficult to accurately parameterize a model.

5. How can the parameterization problem be improved?

The parameterization problem is an ongoing area of research, and scientists are constantly working to improve their methods. Some approaches include incorporating more data and observations into the model, developing more sophisticated algorithms, and using machine learning techniques. Collaborations between different scientific disciplines can also lead to better solutions for addressing the parameterization problem.

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