Another equation of another line

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SUMMARY

The discussion focuses on deriving the parametric and symmetric equations of a line through the point (1, -1, 1) that is parallel to the line defined by the equation $x + 2 = \frac{1}{2}y = z - 3$. Participants emphasize the importance of identifying the direction vector from the given line equation. The correct direction vector is determined to be (2, 1, 1), leading to the formulation of the parametric equations. The discussion concludes with a successful resolution of the problem through a reverse problem-solving strategy.

PREREQUISITES
  • Understanding of parametric equations in three-dimensional space
  • Familiarity with symmetric equations of lines
  • Knowledge of vector representation of lines
  • Ability to manipulate equations to isolate variables
NEXT STEPS
  • Study how to convert between parametric and symmetric forms of a line
  • Learn about direction vectors and their significance in line equations
  • Explore vector calculus concepts related to lines in three-dimensional space
  • Practice solving similar problems involving lines and planes in 3D geometry
USEFUL FOR

Students and educators in mathematics, particularly those studying geometry and vector calculus, as well as anyone seeking to improve their problem-solving skills in three-dimensional line equations.

ineedhelpnow
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Please help, how do I do this?
Find the parametric and symmetric equation for a line through (1,-1,1) and parallel to $x+2= \frac{1}{2}y=z-3$

So confused
 
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ineedhelpnow said:
Please help, how do I do this?
Find the parametric and symmetric equation for a line through (1,-1,1) and parallel to $x+2= \frac{1}{2}y=z-3$

So confused

Parallel lines have the same direction vectors.

Can you get a direction vector for $\displaystyle \begin{align*} x + 2 = \frac{1}{2}y = z - 3 \end{align*}$?
 
That's what I'm stuck on.at first I though it would be v=(-2,2,3) but then I came to the conclusion that it was wrong so I am stuck again.
 
ineedhelpnow said:
That's what I'm stuck on.at first I though it would be v=(-2,2,3) but then I came to the conclusion that it was wrong so I am stuck again.

You need to get better at the problem solving strategy of thinking in reverse. How would you go from a vector form of a line to the symmetric form?

Start by writing out the x, y, z components separately to get the parametric equations.

Solve for t in each equation.

Realise since they are all equal to t, they are equal to each other.

Now how do you think you can go in reverse to get back to the vector equation?
 
i figured it out :)
 

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