# Parametric Equations of a Line

• Jul 3rd 2009, 01:29 PM
Parametric Equations of a Line
I am to find the parametric and vector equations for the line passing through the given points.

P(0, 1/2, 1) Q(2, 1, -3)
The line through the points is parrellel to:
V = rq - rp (q and p are subscripts correponding to points P and Q)
V = < 2-0, 1-1/2, -3-1>
= <2, 1/2, -4>
R= r + Vt
= < 0 , 1/2, 1 > + < 2t , t/2 , -4t >
= < 2t , 1/2 + t/2 , 1-4t >
Parametric equations
x = 2t
y = 1/2 + t/2
z = 1 - 4t
The answer in the book is:

x = 2 + 2t
y = 1 + t/2
z = -3 - 4t

I have done many questions like these and I basically do the same procedure, and I get the correct equations. I don't understand how this particular set of points is different.
• Jul 3rd 2009, 02:08 PM
mr fantastic
Quote:

I am to find the parametric and vector equations for the line passing through the given points.

P(0, 1/2, 1) Q(2, 1, -3)
The line through the points is parrellel to:
V = rq - rp (q and p are subscripts correponding to points P and Q)
V = < 2-0, 1-1/2, -3-1>
= <2, 1/2, -4>
R= r + Vt
= < 0 , 1/2, 1 > + < 2t , t/2 , -4t >
= < 2t , 1/2 + t/2 , 1-4t >
Parametric equations
x = 2t
y = 1/2 + t/2
z = 1 - 4t
The answer in the book is:

x = 2 + 2t
y = 1 + t/2
z = -3 - 4t

I have done many questions like these and I basically do the same procedure, and I get the correct equations. I don't understand how this particular set of points is different.

The parametric equations for a line are not unique. Let t --> t - 1 in your answer and you get the book's answer.
• Jul 3rd 2009, 02:11 PM