Question

Find an equation of the line segment joining the first point to the second point.

(0,0,0) and (1,2,3)

Any thoughts guys.

Answer 1

The answer is evidently \(r(t)=t \langle1,2,3\rangle\), where \(0\le t\le 1\)

Answer 2

I want to know how to get there.
@myininaya
Could you lend a hand?

Answer 3

First, you have to find the direction vector of the equation.
Do you know how?

Answer 4

Not a clue.

Answer 5

Let's think of the points, (0,0,0), and (1,2,3) as the components of 2 vectors.

Answer 6

Let's say that the vector (0,0,0) is OA, and (1,2,3) is OB.

(O=origin)

Answer 7

To find the direction vector, AB, we have to do OB-OA, which is (1,2,3)-(0,0,0), or (1,2,3).

Answer 8

Well that makes more sense... thanks!

Answer 9

Welcome!

Answer 10

What is that interval about though?

Answer 11

Ignore my last reply.
By restricting t from 0 to 1, it defines the line from P to Q.

Answer 12

you have a formula to find it out. It says
\(r(t) = (1-t) r_0+t(r_1)\) \(0\leq t\leq 1\)
your \(r_0 =(0,0,0) ~~and~~r_1=(1,2,3)\)
therefore r(t) = t (1,2,3)