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.

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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.

Mathematics
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|dw:1381002960366:dw|
to add 2 vectors you need to connect them tip to end
Okay, I got that part but was confused where to go from there

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|dw:1381003142681:dw|
Where do I go from there????
drawing part of the question is over, next calculate mag and direction of a+b
That's the part where I'm stuck!
The mag would be found using pythagorean theorem right?
to add vectors, u need to break them into components
add the components bro
?
break vector into x component and y components then add x components and add y components
|dw:1381003391274:dw|
|dw:1381003459892:dw|
Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?
why pythagorean theorem
first find the components of a+b
for the magnitude
x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)
ringt ?
y components are in same direction, so u add them x components are in opposite directions, so u subtract them
How do I know what to subtract from what?
number line :)
|dw:1381003731661:dw|
|dw:1381003758234:dw|
we follow that, if ur components are in that direction, they're +ve if they're in opposite, they're -ve
Okay!
x component of a+b = 4.5cos(60) - 8cos(45) y component of a+b = 4.5sin(60) + 8sin(45)
once you have the x and y components for c, to get direction just use the samne formula, \(\theta = \large \tan^{-1} \frac{y}{x}\)
what about mag?
mag also same formula :- \(\large \sqrt{x^2+y^2}\)
a+b is just a vector, so u can use same formulas
That makes as a lot more sense, thank you so much!
(again!)
np :D
@ganeshie8 I get 25 degrees for angle?
looks wrong
|dw:1381004400621:dw|
check ur calculation again :)
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
ok
@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
The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?
yup !
for mag just take sqrt(x^2+y^2)
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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