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