How to Correctly Parameterize a Line Segment in 3D Space?

[-EquinoX-]

Homework Statement

Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).

Homework Equations

The Attempt at a Solution

I got:

$$\vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k}$$

for some reason webassign tells me it's wrong

 

[tiny-tim]

Hi -EquinoX-!

Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).
…
I got:

$$\vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k}$$

erm … it's minus 2k, isn't it ?

(and some brackets would be a good idea )

 

[-EquinoX-]

Hi -EquinoX-!


erm … it's minus 2k, isn't it ?

(and some brackets would be a good idea )

yes it's -2k, I just mistyped it.. still gives me the wrong answers

 

[sutupidmath]

well, look at it this way.

let r_o=<1,4,-2>, and let u=<5,3,0>. if P1(1,4,-2) and P2(6,7,-2) then as you can see
u=P1P2
Let, r=<x,y,z>

then in general the equation of the line that passes through P1 and whose diercition is along the vector u, is

r=r_o+tu =>

r=i+4j-2k+5ti+3tj=(1+5t)i+(4+3t)j-2k

where 0=<t=<1.

 

[tiny-tim]

… still gives me the wrong answers

In that case, either it doesn't like your absence of brackets, or since it asked for "the line segment from …", it probably expects t to be increasing in that direction.

 

[HallsofIvy]

Homework Statement

Parameterize C, the line segment from the point (1,4,-2) to the point (6,7,-2).

Homework Equations

The Attempt at a Solution

I got:

$$\vec{r}(t) = 6+5t \vec{i} + 7+3t \vec{j} + 2 \vec{k}$$

for some reason webassign tells me it's wrong

that doesn't even make sense. You are adding numbers to vectors. Do you mean
$$\vec{r}(t)= (6+ 5t)\vec{i}+ (7+ 3t)\vec{j}- 2\vec{k}$$