AkashdeepDeb
  • AkashdeepDeb
Help needed. Find the vector sum of the forces \(\vec{A}\) and \(\vec{B}\). \(\vec{| A |}\) is 130N and is along \(\vec{OA}\) where A is (3,-4,12) and \(\vec{| B |}\) = 200N and is along vector \(\vec{PQ}\) where \(\vec{P}\) is (-2,4,7) and Q is (-2,8,10). DO NOT SOLVE IT. Only tell me the concept here. :D
Physics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Draw a coordinate system and then put vectors on ...
AkashdeepDeb
  • AkashdeepDeb
Yes I tried. Can you show it to me once?
AkashdeepDeb
  • AkashdeepDeb
@Saeeddiscover ?

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AkashdeepDeb
  • AkashdeepDeb
@.Sam. ? @experimentX ? :D
anonymous
  • anonymous
To add vectors, you need to put them at a common point without changing their directions.The vector OA makes no difficulty, you may calculate the direction of vector PQ in space, and then catch it to put in the origin.
AkashdeepDeb
  • AkashdeepDeb
Why have they specified their Magnitudes? And what is O in OA?
anonymous
  • anonymous
O just refers to the point (0,0,0). you might calculate the directional angles to find its direction into space...
AkashdeepDeb
  • AkashdeepDeb
And why are the magnitudes given? I mean How is the magnitude of A = 120N ?
anonymous
  • anonymous
Each of the coordinate axes are written in terms of newton rather than meter.
AkashdeepDeb
  • AkashdeepDeb
No I mean Is \(\vec{A}\) = 3i - 4j + 12k ? If yes then HOW IS ITS MAGNITUDE 120?
AkashdeepDeb
  • AkashdeepDeb
130 sry.
AkashdeepDeb
  • AkashdeepDeb
@Saeeddiscover ?
anonymous
  • anonymous
The magnitude of any vector can be obtained using the relation |A|=(a1^2+a2^2+...+an^2)1/2 But in this example, we obtain sth different. Maybe you need to scale the coordinates ...
AkashdeepDeb
  • AkashdeepDeb
Yes man I know that! It is just that after I calculated the displacement vector for PQ I am not getting the magnitude as 200N And even after scaling OA I did not get 130N, What seems to be the problem here chief? :D
AkashdeepDeb
  • AkashdeepDeb
?
anonymous
  • anonymous
For OA and PQ, we have: |OA|=(3^2+4^2+12^2)^1/2=13 |PQ|=[(-2--2)^2+(8-4)^2+(10-7)^2]^1/2=5 If we multiply OA in 10 we get 130.....
AkashdeepDeb
  • AkashdeepDeb
And is it the same for PQ?
AkashdeepDeb
  • AkashdeepDeb
It is NOT! So now what? These has to be a reason they gave the magnitudes! :/
AkashdeepDeb
  • AkashdeepDeb
@Saeeddiscover ?
AkashdeepDeb
  • AkashdeepDeb
@thomaster ?
AkashdeepDeb
  • AkashdeepDeb
@Yahoo! HELP? No help on YahooAnswers too! ^_^ :D Haha..My corny puns! :D
AkashdeepDeb
  • AkashdeepDeb
@Preetha ? @terenzreignz ? @thomaster ?
AkashdeepDeb
  • AkashdeepDeb
@radar ? @goformit100 ? @somebodyhelpmeee.... :/
AkashdeepDeb
  • AkashdeepDeb
@AravindG ?
anonymous
  • anonymous
wat u really want here ?
AkashdeepDeb
  • AkashdeepDeb
The vector sum of the 2 vectors! :/
AkashdeepDeb
  • AkashdeepDeb
Please tell me the question is wrong!! :/ I ahve been at it for a long time
anonymous
  • anonymous
No,I think that the question is correct :P ... but I can't solve "3D coordinate system" and i'm not very good at it,sorry :(
AkashdeepDeb
  • AkashdeepDeb
It is fine. Thanks Stephen Hawking! :D
anonymous
  • anonymous
i dont thik so hw will |B| = 200N?
AkashdeepDeb
  • AkashdeepDeb
The book says it. :/ Do you think it should be 50N?
anonymous
  • anonymous
wat shuld be ur answer?
anonymous
  • anonymous
i mean the net force
AkashdeepDeb
  • AkashdeepDeb
sqrt 234.
anonymous
  • anonymous
the resultant vector b/w two vectors at an angle theta is V= sqrt(A^2 + B^2 +2AB cos theta)
anonymous
  • anonymous
i think u have to find cose theta form given expression and subs
AkashdeepDeb
  • AkashdeepDeb
No actually I just add the 2 vectors! And then I got 3i + 15k
AkashdeepDeb
  • AkashdeepDeb
Sorry....What I mean to say is that... I just added the two vectors with their vector components OA + PQ and then I got the vector = 3i + 15k So then I got the magnitude as sqrt 234!! :D
AkashdeepDeb
  • AkashdeepDeb
@Yahoo! I don't get it. :/
experimentX
  • experimentX
first find the vectors and just add it up
AkashdeepDeb
  • AkashdeepDeb
I did. Can you PLEASE just check if my answer is right? THERE IS NO SOLUTION IN THIHS BOOK.
AkashdeepDeb
  • AkashdeepDeb
The thing is how do I find OA? Do I take O as 0? Should O actually be Q? [Considering it is a typo?]
experimentX
  • experimentX
A = 130*(3,-4,12)/sqrt(3^2 + 4^2 + 12^2) = 130*A/|A| B = 200 * (Q - P)/|Q-P| then just add them up
AkashdeepDeb
  • AkashdeepDeb
The question is why are you multiplying the given magnitudes by their ACtual magnitudes?
experimentX
  • experimentX
you are given direction ... to get vector multiply the magnitude by direction.
AkashdeepDeb
  • AkashdeepDeb
But then you are dividing also right?
experimentX
  • experimentX
what is the vector along (1,1,1) whole magnitude is 12?
AkashdeepDeb
  • AkashdeepDeb
Okay so the vector would be i + j +k But direction would be 1/12.1 + 1/12.j + 1/12.k ??
experimentX
  • experimentX
No ...
AkashdeepDeb
  • AkashdeepDeb
Then?
experimentX
  • experimentX
the first thing that comes to your mind is 12*(i + j + k) = 12 i + 12 j + 12 k but if you take its magnitude ... it turns out to be sqrt(12^2 + 12^2 + 12^2) = 12 sqrt(3)
experimentX
  • experimentX
whne you are given direction first, you should normalize it. that means you should find unit vector along that direction.
experimentX
  • experimentX
(1,1,1) is not unit vector. to find unit vector along (1,1,1) you need to divide it by it's magnitude. (1,1,1)/|(1,1,1)| = 1/sqrt(3)(1,1,1) <- now this is unit vector.
experimentX
  • experimentX
then multiply it by 12, you get a vector whose magnitude is 12 and direction is along (1,1,1)
AkashdeepDeb
  • AkashdeepDeb
Multiply this by 12 [1/sqrt(3)(1,1,1)]
AkashdeepDeb
  • AkashdeepDeb
?
experimentX
  • experimentX
yes
AkashdeepDeb
  • AkashdeepDeb
What is (1,1,1) then?
experimentX
  • experimentX
this is just given direction.
AkashdeepDeb
  • AkashdeepDeb
But it is just a POINT.
experimentX
  • experimentX
Oh ... you are not familiar with tuple notation of vector. (1,1,1) = i + j + k
AkashdeepDeb
  • AkashdeepDeb
Not quite.... We have not studied 3D Geometry yet. :/
experimentX
  • experimentX
anyway you got the point right.
AkashdeepDeb
  • AkashdeepDeb
Yes pretty much! And If we are given just one point does that mean that It starts from the origin?
experimentX
  • experimentX
no not quite.
experimentX
  • experimentX
it has to be specified that other end is at origin.
experimentX
  • experimentX
as in your question. I didn't do it becuase i am lazy to type.
AkashdeepDeb
  • AkashdeepDeb
I got that... :D Thanks btw for helping. Should I be knowing 3D Geometry to solve this question?
experimentX
  • experimentX
no .. just use your i,j,k notation instead of (a,b,c)
AkashdeepDeb
  • AkashdeepDeb
Yeah okay. Thanks! :)
experimentX
  • experimentX
fist make the vector OA = 3i-4j+12k then make it unit vector (unit OA)=OA/|OA| then multiply it by magnitude = 130 *(unit OA) then you are done, you can do what is specified.
AkashdeepDeb
  • AkashdeepDeb
Okay.
anonymous
  • anonymous
Have you been satisfied?
AkashdeepDeb
  • AkashdeepDeb
98%
anonymous
  • anonymous
What's still been unsolved?
AravindG
  • AravindG
Sorry I was away at that time.
AkashdeepDeb
  • AkashdeepDeb
It is totally alright! :)

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