Adding Scalar Multiples of Vectors in a Graph

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Paymemoney
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Homework Statement


Draw the vector [tex]\vec{C} = \vec{A}+2\vec{B}[/tex]
Grid diagram with two brown arrows: vector A points right from the top row, labelled A with an arrow, and vector B points left in a lower row, labelled B with an arrow, shorter than A.


Homework Equations


None


The Attempt at a Solution


This is what i have i don't know if it is correct
Grid diagram with three labelled vectors: A pointing right in brown, B pointing left in brown and shorter, and C in black pointing right and longer, all drawn from the grid origin row.


P.S
 
Hi Paymemoney! :smile:

No, that's not right.

When adding vectors, go to the end of the first vector, then tack on the second vector. :wink:
 
Why have you bent it??

Put it back and start again!

(if it's broken, you'll have to pay for it :frown:)
 
how i do this without bending it? So is it only meant to go horizontally?
 
Paymemoney said:
how i do this without bending it? So is it only meant to go horizontally?

Yes, of course. And to the left.
 
so would this be correct.
Grid diagram with three vectors: brown arrow A pointing right, brown arrow B pointing left and shorter, and a black arrow pointing left that is longer than B, drawn on a square grid.


does it matter where you place the vector, because when i placed it in the middle it was incorrect??

Grid diagram with three vectors: brown vector A pointing right along the top row, long blue vector C pointing left, and short brown vector B pointing left below the origin axis, labelled with arrow notation.
 
Hi Paymemoney! :smile:

(just got up :zzz: …)
Paymemoney said:
so would this be correct.

Nooo …

I think I need to give you the answer:

To add two vectors, you must place the "tail" of the second vector against the "head" of the first vector: the sum is then the vector to that point (from where you started).​

(or the other way round, of course: place the "tail" of the first vector against the "head" of the second vector: it makes no difference)

So in this case, you draw A which is an arrow going 4 to the right, then you draw B which is an arrow going 2 to the left, and you draw that 2 starting at the end of the 4, so you end up with an everall vector of A + 2B being 2 to the right.

(this is just like adding vectors to make a triangle, except that in this case the triangle is flat :wink:)
 
tiny-tim said:
So in this case, you draw A which is an arrow going 4 to the right, then you draw B which is an arrow going 2 to the left, and you draw that 2 starting at the end of the 4, so you end up with an everall vector of A + 2B being 2 to the right.
ok, this is what i got from your explanation, so just to make sure i have interpreted your explanation correctly here it is again(hopefully correct -_-).
Grid diagram of vectors: a brown arrow labelled A points right along the upper row, a black arrow labelled C runs left along a lower row, and a short brown arrow points left on the same row as C.


tiny-tim said:
(this is just like adding vectors to make a triangle, except that in this case the triangle is flat :wink:)

yeh, I'm used to looking at the full triangle.
 
Paymemoney said:
ok, this is what i got from your explanation, so just to make sure i have interpreted your explanation correctly here it is again(hopefully correct -_-).

I don't understand what you've done here. :confused:

Start on the axis, draw a blue line for A, then from the end of that draw a red line for 2B. Now draw a green line from the axis to the end of the red line (as if you were completing a triangle).
 
ok here it is

Grid diagram of vectors: brown arrow A points right from the top, brown arrow B points left at upper left, and red, blue and green segments form a right triangle with a vertical blue side and horizontal red base.



why don't you draw it for me coz i don't think I'm getting anyway.
 
after thinking more about it, i have come to a conclusion that this may be the answer but I'm not sure:

Two side-by-side grid diagrams labelled Solution 1 and Solution 2, each showing vectors A and B as brown arrows and a black arrow, drawn on a square grid.
 
No, not right. A is 4 units long and points to the right. B is 1 unit long and points to the left. 2B is 2 units long and points to the left.

For the sum A + 2B, start at 0, go 4 units to the right. Now tack 2B on. Where do you end up? The vector from 0 to where you ended up is A + 2B.

Since all vectors involved here are horizontal, the sum will be a horizontal vector: one that points either to the right or to the left.
 
2B or not 2B ?

Paymemoney said:
What do you mean by "Now tack 2B on"?

Mark44 :smile: means "tail to head" (as I also explained in post #8)
 
ok, i had another go at it, and this is what i got:

Two side-by-side grids showing vectors: a long brown arrow labelled A pointing right along the top, a short brown arrow labelled B pointing left, and a short black arrow pointing right between them.
 
Last edited:
We're 16 posts into this thread, and you still aren't getting it. Why do you have two diagrams? Are we supposed to pick one?

In the right diagram, the resultant (black) vector starts at the right place, but it's too short. In the left diagram, the resultant vector is the right length, but it starts at the wrong place.
 
well i finally got the answer =___=, yeh it took me awhile because i didn't read the answer you gave me correctly. thanks for the help anyways.