Parametric Equation for Line through (1,0,-1) and Parallel to 1/3(x-4)=1/2y=z+2

[TrueStar]

Homework Statement

Find the parametric equation for the line through (1,0,-1) and parallel to the line 1/3(x-4)=1/2y=z+2

Homework Equations

Vector equation - r=ro+tv

Perhaps the scaler equation? I'm not entirely sure.

The Attempt at a Solution

I'm not sure where to begin; I don't see any examples in the textbook to go on. I'm not sure if I can read the line given to me and pull out points to use and then create a vector with it.

Thanks

 

[ehild]

Find the direction vector of the original line from the equations

1/3 (x-4)=t, 1/2 y =t, z+2=t, expressing x, y, z with the parameter t.

ehild

 

[TrueStar]

So when the line is written with the variables all equal to each other, I am to assume each one is actually equal to t?

 

[ehild]

The above expressions of the coordinates x,y,z are all equal, so each of them is equal to the same number, call it t...

ehild

 

[TrueStar]

Ah. I read through the text again and I think I understand how to read the equation better. I was looking for a set of points, but really I can get a vector out of it.

Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.

 

[TrueStar]

Ah. I read through the text again and I think I understand how to read the equation better. I was looking for a set of points, but really I can get a vector out of it.

Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.

 

[ehild]

Anyway, I believe the answer is:
x= 1+3t
y= 2t
z= -1+t

Hopefully I am correct.

You are! Good job!

ehild