
Vector Magnitude
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.

Its basically asking 8+?=16
So the first one. It wouldnt include pythag (Case 2) as it only contains 2 vectors, with no angles or hint of a vector being in a different direction.