# Math Help - Vector Magnitude

1. ## Vector Magnitude

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

Case 1:
$\b{X} + \b{Y} = 16$
$8 + \b{Y} = 16$
$\b{Y} = 8$

Case 2:
$\sqrt{\b{X}^2 + \b{Y}^2} = 16$
$\b{X}^2 + \b{Y}^2 = 16^2$
$\b{X}^2 + \b{Y}^2 = 256$
$64 + \b{Y}^2 = 256$
$\b{Y}^2 = 192$
$\b{Y} = 8\sqrt{3}$

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

2. 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.