Directed Line Segment Joining (1,1,1) to (1,3,1)

[cse63146]

Homework Statement

Find the directed line segment joining (1,1,1) to (1,3,1)

Homework Equations

The Attempt at a Solution

(1,1,1) + (0,2,0)t is that correct?

 

[Hurkyl]

(1,1,1) + (0,2,0)t is that correct?

Is it a directed line segment?
Does it start at (1,1,1)?
Does it end at (1,3,1)?

If so, then it's correct.

 

[HallsofIvy]

Notice the "start and stop". You will need conditions on t as well as, for the "directed" part, something like "as t goes from ___ to ___".

 

[cse63146]

you mean like this:

for all t \rightarrow \Re

or what I am trying to say is that for all t that are real numbers (couldn't find the symbol for it; looks like a small 'e')

 

[HallsofIvy]

No, the whole point is that t cannot be "all real numbers". That could give the entire line, not the line segment. And you still haven't dealt with the "directed" part. Do you understand the difference between a line segment and a line? Do you understand what a directed line or directed line segment is?

 

[cse63146]

0 \leq t \leq 1

 

[HallsofIvy]

Okay, that gives the "segment". Now what about the "directed" part? Unfortunately, your original statement of the problem doesn't give a direction. You just said "the directed line segment joining (1,1,1) to (1,3,1)" which does not state a direction. Is the direction from (1, 1, 1) to (1, 2, 1) or from (1, 2, 1) to (1, 1, 1)?