Question

Can someone explain to me how r = [vector] + t*[vector no. 2] works? Any kind of related info welcome. I need to find how can I identify vector equations that are vector equations for the same line asthe r = [vector] + t*[vector no. 2]? What are the conditions? Thanks a lot, exam tmo..

Answer 1

vector 2 will always be the same (or pointing in the opposite direction)

vector 1 should be the position of a point on the line

Answer 2

Have you seen how two vectors are parallel if one is a scalar multiple of the other? (i.e: [vector 1] = k*[vector 2] for a number k)
The fact that they are parallel means that they have the same direction.

This is just an extension of that, adding in another vector that we travel along before going along a multiple of the second vector.

The family of vectors satisfying r= [vector] + t*[vector no. 2] will just be the ones that travel along [vector], then travel a certain distance in the direction of [vector no. 2].

If you can find an example of a question on this subject it may help your understanding more.

Answer 3

http://tutorial.math.lamar.edu/Classes/CalcII/EqnsOfLines.aspx

Answer 4

phi:for r= \[\left(\begin{matrix}4 \\ 4\end{matrix}\right)\] + t*\[\left(\begin{matrix}3 \\ 1\end{matrix}\right)\] is a vector equation for LINE L. Why are vector equations B and D on the same line? When B is r= \[\left(\begin{matrix}4 \\ 4\end{matrix}\right)\] + t*\[\left(\begin{matrix}6 \\ 2\end{matrix}\right)\] and D is r = \[\left(\begin{matrix}7 \\ 5\end{matrix}\right)\] + t*\[\left(\begin{matrix}3 \\ 1\end{matrix}\right)\

Answer 5

whoopsie so below (7 5) you have the same bracket thing but replace 7 with 3 and 5 with 1 to get (3 1)

Answer 6

"slope vector" for L is (3 1) (transposed, but you get the idea)
as traxter pointed out, the "slope" vector may be scaled by a constant.
in line B, (6 2) is 3*(3 1) so both vectors point in the same direction (B's is bigger but that does not change the direction)
and both equations have (4 4) on the line (set t=0 to see this)

line D
slope vector is (3 1).
now show (7 5) is on line L:
(7 5) = ( 4 4) + t(3 1)
(3 1)= t*(3 1)
t= 1

we already know line B is the same as line L, but you can show (7 5) is on line B
the same way