Writing vector and parametric equations for a line that....

[Specter]

Homework Statement

[/B]
Write vector and parametric equations for the line that goes through the points P(–3, 5, 2) and Q(2, 7, 1).

Homework Equations

The Attempt at a Solution

First I find the direction vector for PQ.

PQ=Q-P = (2,7,1)-(-3,5,2)
=[2-(-3),7-5,1-2]
=5,2,-1

PQ= (5,2,-1)

Now I have a direction vector and two points. I think I can write the vector equation now but I am not sure which point to use, P or Q, and if it matters.

If I were to use P(-3,5,2) the vector equation would look like the following:

(x,y,z)=(-3,5,2)+t(5,2,-1)

Then the parametric equations would be

x=-3+5t
y=5+2t
z=2-t

 

[LCKurtz]

You can check it yourself. Try $t=0$ and $t=1$ to see if it goes through your two points.

 

[Specter]

You can check it yourself. Try $t=0$ and $t=1$ to see if it goes through your two points.

Sorry if this is a dumb question but this is my first math course in... a while. Is this what you meant?

I set t=0 and t=1 for the parametric equations and got the coordinates

t=0, (-3,5,2)
t=1, (2,7,1)

 

[Mark44]

Yes, that's what LCKurtz meant.

I am not sure which point to use, P or Q, and if it matters.

Doesn't matter -- you can use either one.

 

[Specter]

Yes, that's what LCKurtz meant.

Doesn't matter -- you can use either one.

Thank you.

 

[SammyS]

Homework Statement

[/B]
Write vector and parametric equations for the line that goes through the points P(–3, 5, 2) and Q(2, 7, 1).

Homework Equations

The Attempt at a Solution

First I find the direction vector for PQ.

PQ=Q-P = (2,7,1)-(-3,5,2)
=[2-(-3),7-5,1-2]
=5,2,-1

PQ= (5,2,-1)

Now I have a direction vector and two points. I think I can write the vector equation now but I am not sure which point to use, P or Q, and if it matters.

If I were to use P(-3,5,2) the vector equation would look like the following:

(x,y,z)=(-3,5,2)+t(5,2,-1)

Then the parametric equations would be

x=-3+5t
y=5+2t
z=2-t

Well, I wrote this reply and failed to actually post it.
Doesn't really say anything much different than what the others said.
...

Your results look fine.

It does not matter which of the points you start with. In fact you can find some other point on this line and use that.

Using s as the parameter, start at point Q: (2, 7, 1) .