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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.
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Study23
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dav21
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to add 2 vectors you need to connect them tip to end
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Okay, I got that part but was confused where to go from there
dav21
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Where do I go from there????
ganeshie8
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drawing part of the question is over,
next calculate mag and direction of a+b
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That's the part where I'm stuck!
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The mag would be found using pythagorean theorem right?
ganeshie8
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to add vectors,
u need to break them into components
dav21
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add the components bro
Study23
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?
dav21
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break vector into x component and y components then add x components and add y components
ganeshie8
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ganeshie8
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Study23
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Oh okay! So from there, I would use the pythagorean theorem, and for the direction, I would...?
dav21
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why pythagorean theorem
ganeshie8
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first find the components of a+b
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for the magnitude
ganeshie8
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x component of a+b = 4.5cos(60) - 8cos(45)
y component of a+b = 4.5sin(60) + 8sin(45)
ganeshie8
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ringt ?
ganeshie8
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y components are in same direction, so u add them
x components are in opposite directions, so u subtract them
Study23
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How do I know what to subtract from what?
ganeshie8
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number line :)
ganeshie8
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ganeshie8
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ganeshie8
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we follow that,
if ur components are in that direction, they're +ve
if they're in opposite, they're -ve
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Okay!
ganeshie8
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x component of a+b = 4.5cos(60) - 8cos(45)
y component of a+b = 4.5sin(60) + 8sin(45)
ganeshie8
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once you have the x and y components for c,
to get direction just use the samne formula, \(\theta = \large \tan^{-1} \frac{y}{x}\)
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what about mag?
ganeshie8
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mag also same formula :- \(\large \sqrt{x^2+y^2}\)
ganeshie8
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a+b is just a vector, so u can use same formulas
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That makes as a lot more sense, thank you so much!
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(again!)
ganeshie8
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np :D
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@ganeshie8 I get 25 degrees for angle?
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@ganeshie8 ?
ganeshie8
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looks wrong
ganeshie8
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ganeshie8
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check ur calculation again :)
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ok
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@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
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The magnitudes is what I'm having trouble with. When I use the formula, I get a decimal answer?
ganeshie8
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yup !
ganeshie8
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for mag just take sqrt(x^2+y^2)