Question:

A vector $\displaystyle \b{X}$ with a magnitude of $\displaystyle 8$, when combined with vector $\displaystyle \b{Y}$ has a sum of magnitude $\displaystyle 16$. What is the value of $\displaystyle \b{Y}$?

Case 1:

$\displaystyle \b{X} + \b{Y} = 16$

$\displaystyle 8 + \b{Y} = 16$

$\displaystyle \b{Y} = 8$

Case 2:

$\displaystyle \sqrt{\b{X}^2 + \b{Y}^2} = 16$

$\displaystyle \b{X}^2 + \b{Y}^2 = 16^2$

$\displaystyle \b{X}^2 + \b{Y}^2 = 256$

$\displaystyle 64 + \b{Y}^2 = 256$

$\displaystyle \b{Y}^2 = 192$

$\displaystyle \b{Y} = 8\sqrt{3}$

Confusion:

Which case it it or is it something completely different? The wording is confusing me. Thanks in advance.