Equations for a Line Passing Through Two Given Points in 3D Space

[somebodyelse5]

Homework Statement

Find the vector and parametric equations for the line through the point P(-3, 3, -5) and the point Q(-7, 4, -1).

Homework Equations

N/A

The Attempt at a Solution

r= <__,__,-5>+t<__,__,4> The -5 and 4 are given.

Heres what I have so far. r=<-3,3-5>+t<__,__,__>

I am totally lost on how to find those other two points and the equations.

 

[Mark44]

Homework Statement

Find the vector and parametric equations for the line through the point P(-3, 3, -5) and the point Q(-7, 4, -1).

Homework Equations

N/A

The Attempt at a Solution

r= <__,__,-5>+t<__,__,4> The -5 and 4 are given.

Heres what I have so far. r=<-3,3-5>+t<__,__,__>

I am totally lost on how to find those other two points and the equations.

Think of it in terms of adding vectors - one vector from the origin to a given point on the line, and another vector from the given point on the line to an arbitrary point on the line.

Your vector equation of the line will be r = OP + t*PQ

What you're missing is a vector that gives the direction of the line.

 

[somebodyelse5]

Think of it in terms of adding vectors - one vector from the origin to a given point on the line, and another vector from the given point on the line to an arbitrary point on the line.

Your vector equation of the line will be r = OP + t*PQ

What you're missing is a vector that gives the direction of the line.

Ok, Is the value of 4, which is givin in the problem as the z value in the second vector, a clue at all?

I tried multiplying P and Q and then dropping them all down so that they agree with the z=4 value and that didnt work. Its not that simple is it? PQ doesn't mean I can just multiply P and Q together does it?

 

[Mark44]

How do you find the vector from P to Q? You don't multiply - that makes no sense at all.

 

[somebodyelse5]

How do you find the vector from P to Q? You don't multiply - that makes no sense at all.

Oh ok, I am still thinking in basic algebra. Not much time spent on vectors yet.

So I would to Q-P to get PQ.

 

[Mark44]

Yes.