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Give me a standpoint and I will move the earth. ...Archimedes (287-212BC)

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 Author Topic: Vector Addition  (Read 280249 times) 0 Members and 2 Guests are viewing this topic. Click to toggle author information(expand message area).
faran
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 « Embed this message 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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 « Embed this message 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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 « Embed this message 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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 « Embed this message Reply #33 on: July 08, 2011, 02:57:45 am » posted from:-,-,PAKISTAN

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Fu-Kwun Hwang
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 « Embed this message 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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 « Embed this message 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

HERE BOLD CHARACTERS REPRESENT VECTORS.
 « Last Edit: January 02, 2012, 01:45:26 pm by THERITESHBABA » Logged
THERITESHBABA
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 « Embed this message 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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 « Embed this message 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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 « Embed this message Reply #38 on: December 29, 2012, 01:13:07 pm » posted from:,,Satellite Provider

thanks
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Give me a standpoint and I will move the earth. ...Archimedes (287-212BC)
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