Parametric Equations for Line PQ: Find Solution

In summary, the parametric equations for the line joining the points P = (1,2,-1) and Q = (5,7,5) can be written as x = 1+4t, y = 2+5t, and z = -1+6t, where t is a scalar. This was marked wrong by the teacher, who noted that "line PQ = <4,5,6> is the normal" and deducted points from the student's test score. However, it appears that the equations are correct and there is no error in the student's work. Other students also agree that the answer is correct.
  • #1
major_maths
30
0
1. Find parametric equations for the line joining the points P = (1,2,-1) and Q = (5,7,5).[/b]

2. x = x0+ta
y = y0+tb
z = z0+tc

3. v = <(5-1), (7-2), (5+1)>
so v = <4,5,6> and since v is a vector in the direction of the line and should be able to be placed in the above equations in place of <a,b,c> and either of the point (P or Q) should be placed in the values of x0, y0, and z0. This should result in the final parametric equations:

x = 1+4t
y = 2+5t
z = -1+6t

This is a problem on one of my tests but my teacher marked it wrong, noting that "line PQ = <4,5,6> is the normal" and marked off 6 points out of 10. I've got no clue what I did wrong.
 
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  • #2
I don't see anything wrong with that.
 
  • #3
Hm, I'm a student myself but that looks correct to me...

I would've done the same thing!
 

1. What are parametric equations?

Parametric equations are a set of equations that express a set of quantities as functions of one or more independent variables, known as parameters. These equations are commonly used to represent curves and lines in the Cartesian coordinate system.

2. How do parametric equations help in finding solutions for line PQ?

Parametric equations provide a way to represent the coordinates of points on a line in terms of a parameter, such as time or distance. By setting the parameter to different values, we can generate a set of points that lie on the line PQ. By finding the common values for the coordinates of these points, we can determine the solution for line PQ.

3. Can parametric equations be used for non-linear lines?

Yes, parametric equations can be used for both linear and non-linear lines. The equations may be more complex for non-linear lines, but the concept of using a parameter to represent the coordinates of points remains the same.

4. How do I determine the parameter for a given line PQ?

The parameter for a line PQ can be determined by selecting a starting point on the line and assigning a value to the parameter. The parameter can then be incremented or decremented to generate additional points on the line.

5. Are there any limitations to using parametric equations for line PQ?

One limitation of using parametric equations for line PQ is that they are not unique. This means that there may be multiple sets of parametric equations that can represent the same line. It is important to carefully choose the parameter and starting point to ensure accuracy in finding the solution.

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