Simple vector addition question

[christinaa_s]

just a quick question, I've never dealt with vectors before, they say you are simply supposed to add them, the same way you would add any two numbers, ie: a + b = c
yet whenever they add two vectors, they end up with a different sum..
ie: 1m + 2.5m = 7m
this seems so simple, what am I missing?

 

[rdt2]

Suppose you go 3m east then turn and go 4m north. How far from your starting point are you? 7m ? Or 5m ?

Suppose you go 3 m east then turn and go 3 m west. How far from your starting point are you? 6m ? Or 0m ?

The essential thing about a vector is that it points in a particular direction and you have to take account of this direction when adding vectors.

 

[arildno]

christina:
You are probably misunderstanding the addition principle of vectors to mean you can add the lengths of two vectors to get the length of the new one.
This is untrue!

 

[christinaa_s]

thanx for both your responses.

rdt2, i understand the second question, the final displacement, if u go 3m east than 3m west, you are back in the same place, making the sum o
if u add them together its (-3) + (3) leading to 0.

but if u go 3m (east) and 4m (north) , how do you get the sum to total up to 5m?
aren't north and east positive numbers?


also if i am not supposed to be adding the vector lengths (m) what am i supposed to be adding?

 

[Hootenanny]

but if u go 3m (east) and 4m (north) , how do you get the sum to total up to 5m?
aren't north and east positive numbers?

Try drawing out the paths. Draw a dot as your starting point. Then draw a line horizontally east of length 3cm. Draw another dot at the end of this line. From this point, draw a vertical line north of length 4cm, place a dot at the end of this line. Now draw a straight line from your finnishing point to your starting point. How long is this line?

-Hoot

 

[BobG]

Maybe this will give you a feel for what you're trying to do.

http://comp.uark.edu/~jgeabana/java/VectorCalc.html

Mathematically, you want to break each vector down into Cartesian coordinates (x and y components). Add the x's together; add the y's together; and you have your result in Caresian coordinates. To get the magnitude of the resulting vector, plug the new x and y components into the Pythagorean Theorem.

 

[christinaa_s]

hootenanny: i still have absolutely no idea how you can get 5, from adding 3 and 4. if you draw a line connecting the beginning to the end, i just don't get it! i am definitely missing something. however i understand how you could get five if you use the pythagoream theorum (sp) to solve for the hypotenuse..

i feel like the solution to my question is so simple, and i am just missing some vital information, or rules.. i never took algebra, geometry, trigonometry, or any physics classes before this grade 12 physics that i am taking right now, so i am unaware of most of the concepts.

 

[Hootenanny]

hootenanny: i still have absolutely no idea how you can get 5, from adding 3 and 4. if you draw a line connecting the beginning to the end, i just don't get it! i am definitely missing something. however i understand how you could get five if you use the pythagoream theorum (sp) to solve for the hypotenuse..

Drawing out the triangle (what I told you to do) is the same as using pythag. With vector you have to consider their direction in addition to their magnitude.

 

[Hootenanny]

Try this website, I think it explains the basics pretty well;

http://www.cartage.org.lb/en/themes/Sciences/Mathematics/OddsEnds/vector/introvector.html

 

[christinaa_s]

i read the webpage, it was helpful thanx.