Vector Construction help! I've been stuck on this for some time, not sure what to do! Construct c = a + b by drawing and calculating the direction and magnitude of c. The direction should be measured from the +axis. // See illustration below.

- anonymous

- katieb

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- anonymous

|dw:1381002960366:dw|

- anonymous

to add 2 vectors you need to connect them tip to end

- anonymous

Okay, I got that part but was confused where to go from there

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## More answers

- anonymous

|dw:1381003142681:dw|

- anonymous

Where do I go from there????

- ganeshie8

drawing part of the question is over,
next calculate mag and direction of a+b

- anonymous

That's the part where I'm stuck!

- anonymous

The mag would be found using pythagorean theorem right?

- ganeshie8

to add vectors,
u need to break them into components

- anonymous

add the components bro

- anonymous

?

- anonymous

break vector into x component and y components then add x components and add y components

- ganeshie8

|dw:1381003391274:dw|

- ganeshie8

|dw:1381003459892:dw|

- anonymous

Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?

- anonymous

why pythagorean theorem

- ganeshie8

first find the components of a+b

- anonymous

for the magnitude

- ganeshie8

x component of a+b = 4.5cos(60) - 8cos(45)
y component of a+b = 4.5sin(60) + 8sin(45)

- ganeshie8

ringt ?

- ganeshie8

y components are in same direction, so u add them
x components are in opposite directions, so u subtract them

- anonymous

How do I know what to subtract from what?

- ganeshie8

number line :)

- ganeshie8

|dw:1381003731661:dw|

- ganeshie8

|dw:1381003758234:dw|

- ganeshie8

we follow that,
if ur components are in that direction, they're +ve
if they're in opposite, they're -ve

- anonymous

Okay!

- ganeshie8

x component of a+b = 4.5cos(60) - 8cos(45)
y component of a+b = 4.5sin(60) + 8sin(45)

- ganeshie8

once you have the x and y components for c,
to get direction just use the samne formula, \(\theta = \large \tan^{-1} \frac{y}{x}\)

- anonymous

what about mag?

- ganeshie8

mag also same formula :- \(\large \sqrt{x^2+y^2}\)

- ganeshie8

a+b is just a vector, so u can use same formulas

- anonymous

That makes as a lot more sense, thank you so much!

- anonymous

(again!)

- ganeshie8

np :D

- anonymous

@ganeshie8 I get 25 degrees for angle?

- anonymous

@ganeshie8 ?

- ganeshie8

looks wrong

- ganeshie8

|dw:1381004400621:dw|

- ganeshie8

check ur calculation again :)

- ganeshie8

wolfram says below :-
http://www.wolframalpha.com/input/?i=arctan%28%284.5sin%2860%29+%2B+8sin%2845%29%29%2F+%284.5cos%2860%29+-+8cos%2845%29%29%29
add 180 to it, to get into 2nd quadrant maybe

- anonymous

ok

- anonymous

@ganeshie8 What about if the vectors are being substracted then what do you do with the components for a and b? Is it the same like: we follow that,
if ur components are in that direction, they're +ve
if they're in opposite, they're -ve

- anonymous

The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?

- ganeshie8

yup !

- ganeshie8

for mag just take sqrt(x^2+y^2)

- ganeshie8

http://www.wolframalpha.com/input/?i=sqrt%28%284.5sin%2860%29+%2B+8sin%2845%29%29%5E2%2B%284.5cos%2860%29+-+8cos%2845%29%29%5E2%29

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