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Author Topic: Vector Addition  (Read 268174 times)
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faran
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Reply #30 on: July 06, 2011, 03:34:59 am » posted from:-,-,PAKISTAN

Hi folk, I need help.
I encountered a question in my high school exam that was

" The resultant of two anti-parallel vectors A and B is:
1) A+B
2) A-B "

What is the correct answer?
I was told that it is A-B, but how could it be A-B, when resultant it self means that it is bascially the addition of two vectors.
If B vector is anti to A, then it should be -B as convention, but what if we say that -B=C
Then it becomes A+C, means we have to add them both to get answer.
I'm stuck please help me out.
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Fu-Kwun Hwang
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Reply #31 on: July 06, 2011, 06:28:00 pm » posted from:Taipei,T'ai-pei,Taiwan

two anti-parallel vectors \vec{A} and \vec{B} means \vec{B}=-\vec{A}

The sum of two vectors \vec{A} and \vec{B} is \vec{A}+\vec{B}= \vec{A}+(-\vec{A})=\vec{0}
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faran
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Reply #32 on: July 07, 2011, 03:05:59 am » posted from:-,-,PAKISTAN

Thanks for the response.
But what if the two vectors are of different magnitude and are anti parallel.
Then infact we'll have to subtract their magnitudes that will be |A-B| , but what if we want to write them in vector form, what would we write them if we want to get resultant?

A-B
or
A+B

Some people told me that as they are anti-parallel, then their resultant will be ultimately
A+(-B),
i.e A-B

One of my friend argued that the resultant should be A+B because

Let two vectors A and B,
A= |A| (k )
B= |B| (-k)

Now
Resultant:

A + (-B)

[|A| (k)] + [|B| (-k)]

As |B|(-k)= B

so

A + B
----
Now if it is A+B, then it means that they would be added to each other, and their magnitutude should also be added?

Please do try to understand what I've written, and help me.
Waiting for the reply
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faran
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Reply #33 on: July 08, 2011, 02:57:45 am » posted from:-,-,PAKISTAN

Huh
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Fu-Kwun Hwang
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Reply #34 on: July 08, 2011, 04:32:35 pm » posted from:Taipei,T'ai-pei,Taiwan

The sum of two vectors is always \vec{A}+\vec{B}.
 
For example: if \vec{B}=-0.2 \vec{A}
 \vec{A}+\vec{B}=\vec{A}+ (-0.2\vec{A})=0.8 \vec{A} (1.0-0.2)
 
if\vec{B}= 0.2 \vec{A} , two vector are parallel.
 \vec{A}+\vec{B}=\vec{A}+ (0.2\vec{A})=1.2 \vec{A} (1.0+0.2)
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THERITESHBABA
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Reply #35 on: January 02, 2012, 12:35:36 pm » posted from:Kolkata,West Bengal,India

if the angle between two vectors is a & b is @ and angle between vectors a+b and a is O
then
  
tan@=(bsinO )/(a+bcosO )
now
tan2 @=(bsinO)2/(a+bcosO)2

 now
tan2@= sec2@ -1
and
sec2@ =1/cos2@
{a2 sec2O + b2 + 2absecO}
so cos2@=
____________________________________________________________________
{a2sec2O + b2sec2O + 2absecO}


if @ =0
b2=b2cos2O
O=0
if @ =90
a=-bcosO
if O=90
  
-b2
tan2@=
____
a2+b2




Smiley Wink Cheesy Grin HERE BOLD CHARACTERS REPRESENT VECTORS.
« Last Edit: January 02, 2012, 01:45:26 pm by THERITESHBABA » Logged
THERITESHBABA
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Reply #36 on: January 02, 2012, 01:48:13 pm » posted from:Kolkata,West Bengal,India

if the angle between two vectors is a & b is @ and angle between vectors a+b and a is O
then
 

tan@=(bsinO )/(a+bcosO )

now

tan2 @=(bsinO)2/(a+bcosO)2


 now

tan2@= sec2@ -1

and

sec2@ =1/cos2@

 

 

{a2 sec2O + b2 + 2absecO}

so cos2@=

 

{a2sec2O + b2sec2O + 2absecO}





 


if @ =0

 

b2=b2cos2O

 

O=0

 

if @ =90

 

a=-bcosO

 

if O=90


 

-b2

 

tan2@=  _________________

 

 

a2+b2

 

 
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nateuer
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Reply #37 on: November 17, 2012, 09:42:01 pm » posted from:Dhaka,Dhaka,Bangladesh

-*-
I have just seen it,nice I love that.
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koclup1580
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Reply #38 on: December 29, 2012, 01:13:07 pm » posted from:,,Satellite Provider

thanks
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