# Vector problem

1. Aug 16, 2016

### gracy

1. The problem statement, all variables and given/known data
If the angle between two vectors A and B is 120 , it's resultant C will be
a)C = I A - B I
b)C< I A - B I
c)C> I A -B I
d)C= I A + BI

2. Relevant equations
R= √A ^2 + B^2 + 2AB Cos θ

3. The attempt at a solution
C=√ A^2 +B^2 + 2AB Cos 120
= √A^2 + B^2 -2AB 1/2
= √A ^2 + B^2 - AB
I don't know √A ^2 + B^2 - AB is greater or lesser than I A -B l & I A + B l

2. Aug 16, 2016

### BvU

Where's the drawing ?

And it's time for you to switch to a notation where you can distinguish vectors ($\vec A$) from numbers ($|\vec A|$). Now it's messy.

3. Aug 16, 2016

### Isaac0427

There is a theorem requarding this. Set up the "equations"
$A^2+B^2-AB ? |A+B|$
And
$A^2+B^2-AB ? |A-B|$

To get the theorem, square both sides of the question marks (if you don't know how to work with the absolute value, just treat it as parentheses and say that A and B are positive numbers. It won't always work but it does with this). Then, use logic to find if ? is =,> or <.

4. Aug 16, 2016

### David Lewis

Some problems can be solved immediately by inspection -- no calculations needed.
We know the resultant is going to be A + B in all cases.
Because the angle between vectors is 120o, and we're only concerned with the magnitude of the resultant, more than one answer choice may be correct.

Last edited: Aug 16, 2016
5. Aug 16, 2016

### gracy

$A^4+B^4-A^2B ^2< |A^2 +B^2 + 2AB |$

$A^4+B^4-AB > |A^2-B^2 -2AB|$

But in my question it is in square roots.

First we will remove square roots for this square both the sides

$A^2+B^2-AB ? |A^2+B^2 + 2AB|$

No prize for guessing $A^2+B^2-AB < |A^2+B^2 + 2AB|$
Similarly
$A^2+B^2-AB > |A^2+B^2 - 2AB|$
Hence option C.
Right?

6. Aug 16, 2016

### gracy

Which theorem is it?

7. Aug 16, 2016

### Isaac0427

You just found it! Option C is correct, but you did make a mistake in your math.
$|A+B|^2=|A^2|+|B^2|+|2AB|$
The way you did it, the sign would be wrong if A or B were negative. As I said, this is the same as $|A|^2+|B|^2+2|A||B|$

8. Aug 16, 2016

### cnh1995

=√(A2+B2-2AB+AB)..

9. Aug 16, 2016

### Isaac0427

Right, I forgot the square root.

10. Aug 16, 2016

### gracy

What's this?

11. Aug 16, 2016

### BvU

It's called a hint

12. Aug 16, 2016

### gracy

Is your "hint" supposed to take me on any helpful page ? I am unable to click on it though.

13. Aug 16, 2016

### BvU

It's not my hint, it's cnh's hint. You are supposed to recognize $A^2 - 2AB + B^2$ as $(A-B)^2$.

14. Aug 16, 2016

### gracy

But there is + AB as well .

15. Aug 16, 2016

### BvU

Yes. So $C^2 = (A-B)^2$ plus a little leftover. That is one of your choices in the original exercise. Are we still looking at what we are doing, or are we too busy responding instantaneously to any post that tries to help us further ?

And in PF, hyperlinks are blue. Underlining conveys emphasis