Calc III. Vectors and the Geometry of Space

[perc_wiz11]

Homework Statement

Use vectors to find the points of trisection of the line segment with endpoints (1,2) and (7,5).

Homework Equations

Not sure.

The Attempt at a Solution

I don't really know where to start. i tried to create a standard vector equation but its a line segment not a vector.

please help when possible.

 

[Kurdt]

If you had two position vectors a and b, then how could you describe the line segment in terms of these vectors? Then what do you imagine the coordinates of position vectors at the trisection points will be?

 

[perc_wiz11]

answer question?

once i create a standard vector, can say that the points of trisection are at the scalar multiples of v? then translate them back to the line segment at its original position? so if the standard vector is <6,3> and take 1/3 v the points of trisection on that vector are (2,1) and (4,2). once i translate that, would the answer be (3,3) and (5,4) ?

 

[HallsofIvy]

once i create a standard vector, can say that the points of trisection are at the scalar multiples of v?

Not without saying what v is!

then translate them back to the line segment at its original position? so if the standard vector is <6,3> and take 1/3 v the points of trisection on that vector are (2,1) and (4,2). once i translate that, would the answer be (3,3) and (5,4) ?

Is v the vector from (1, 2) to (7, 5)? If so, then what you are doing is correct and you have the right answer.