# Thread: addition: magnitude of a vector

1. ## addition: magnitude of a vector

Given $\displaystyle \mid \overline{a}\mid=3, \mid \overline{b}\mid=5$ and $\displaystyle \mid \overline{a}+\overline{b}\mid=7$, determine $\displaystyle \mid \overline{a}-\overline{b}\mid$

2. Originally Posted by juanfe_zodiac
Given $\displaystyle \mid \overline{a}\mid=3, \mid \overline{b}\mid=5$ and $\displaystyle \mid \overline{a}+\overline{b}\mid=7$, determine $\displaystyle \mid \overline{a}-\overline{b}\mid$
Here's a hint, see where you can get with it

$\displaystyle | \overline a - \overline b |^2 = | \overline a |^2 - 2 \overline a \cdot \overline b + | \overline b |^2$

and

$\displaystyle | \overline a + \overline b |^2 = | \overline a |^2 + 2 \overline a \cdot \overline b + | \overline b |^2 \implies 2 \overline a \cdot \overline b = | \overline a + \overline b |^2 - | \overline a |^2 - | \overline b |^2$

3. Originally Posted by Jhevon
Here's a hint, see where you can get with it

$\displaystyle | \overline a - \overline b |^2 = | \overline a |^2 - 2 \overline a \cdot \overline b + | \overline b |^2$

and

$\displaystyle | \overline a + \overline b |^2 = | \overline a |^2 + 2 \overline a \cdot \overline b + | \overline b |^2 \implies 2 \overline a \cdot \overline b = | \overline a + \overline b |^2 - | \overline a |^2 - | \overline b |^2$

still lost...i dont know why you are raising them to the power of 2...

4. Originally Posted by juanfe_zodiac
still lost...i dont know why you are raising them to the power of 2...
...you were given numerical values for most of what you see in my post. raise them to 2 as you would any other number. for instance, wherever you see $\displaystyle | \overline a |$ you can write 3 instead

5. Originally Posted by Jhevon
...you were given numerical values for most of what you see in my post. raise them to 2 as you would any other number. for instance, wherever you see $\displaystyle | \overline a |$ you can write 3 instead

is the answer 34??? i reemplaced 3 and 5 where the a's and the b's were thats what i got...i dont think im right...

6. Originally Posted by juanfe_zodiac
is the answer 34??? i reemplaced 3 and 5 where the a's and the b's were thats what i got...i dont think im right...
no, that's not right. what equation did you place them in?

7. Originally Posted by Jhevon
no, that's not right. what equation did you place them in?
$\displaystyle \implies 2 \overline a \cdot \overline b = | \overline a + \overline b |^2 - | \overline a |^2 - | \overline b |^2$

i found $\displaystyle a^2-b^2$

8. Originally Posted by juanfe_zodiac
$\displaystyle \implies 2 \overline a \cdot \overline b = | \overline a + \overline b |^2 - | \overline a |^2 - | \overline b |^2$
first of all, you would not get 34 by plugging in the values we are given. secondly, you are looking for $\displaystyle | \overline a - \overline b|$ not $\displaystyle 2 \overline a \cdot \overline b$

9. Originally Posted by Jhevon
first of all, you would not get 34 by plugging in the values we are given. secondly, you are looking for $\displaystyle | \overline a - \overline b|$ not $\displaystyle 2 \overline a \cdot \overline b$

i dont know where am i going to get this $\displaystyle | \overline a - \overline b|$ from those formulas...help me plzz

10. Originally Posted by juanfe_zodiac
i dont know where am i going to get this $\displaystyle | \overline a - \overline b|$ from those formulas...help me plzz
i am helping. did you read my post? try to follow the logic here.

i gave you the formula for $\displaystyle |\overline a - \overline b|^2$, you only need to square root both sides to find $\displaystyle |\overline a - \overline b|$.

the problem is, the equation has $\displaystyle 2 \overline a \cdot \overline b$ in it, which we know nothing about. my last equation shows how to calculate it using values we know so that we can plug it into the first equation

11. Originally Posted by Jhevon
i am helping. did you read my post? try to follow the logic here.

i gave you the formula for $\displaystyle |\overline a - \overline b|^2$, you only need to square root both sides to find $\displaystyle |\overline a - \overline b|$.

the problem is, the equation has $\displaystyle 2 \overline a \cdot \overline b$ in it, which we know nothing about. my last equation shows how to calculate it using values we know so that we can plug it into the first equation

the answer was there all the time...thank you and sorry for wasting your time....i got the answer....algebra is just magic...(4.36)

12. Originally Posted by juanfe_zodiac
the answer was there all the time...thank you and sorry for wasting your time....i got the answer....algebra is just magic...(4.36)
leave it as $\displaystyle \sqrt {19}$

13. i gave this problem to someone today and i came up with a new solution. this one is geometrical.

i won't say what the solution is, i will just say it involves using the law of cosines with the diagram below as a guide.

14. Originally Posted by Jhevon
i gave this problem to someone today and i came up with a new solution. this one is geometrical.

i won't say what the solution is, i will just say it involves using the law of cosines with the diagram below as a guide.

someone also used a metod that had to deal with coordenates...xyz...but basicly is the same thing as what you did...but he used coordinates because he said that we cannot do the factorization thing because we are trying to find magnitude, a number and we cant spilt it the vectors like that because is a number...but he got the same answer as you did...thats weird...thanks for the new method

15. Originally Posted by juanfe_zodiac
someone also used a metod that had to deal with coordenates...xyz...but basicly is the same thing as what you did...but he used coordinates because he said that we cannot do the factorization thing because we are trying to find magnitude, a number and we cant spilt it the vectors like that because is a number...but he got the same answer as you did...thats weird...thanks for the new method
i'd like to see that solution. coming up with coordinates for this seems like a pain. it is much easier to just draw an informal diagram as i did. you get to the same conclusion with less work. to come up with the coordinates, you probably have to do some of the things i did here anyway.

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