<s>[INST] Vectors Year 11 
This is a vectors question I got, could any confirm my answer? I got $6.066\underline i - 279.28\underline j$.
$AB = \underline B  - \underline A $
(Working on Vector $\underline B$) 
\begin{align}x &= |B|\cos \theta \\
x &= 150\cos 315 \\
x &= 75\sqrt 2 \end{align}
\begin{align}y &= |B|\sin \theta \\
y &= 150\sin 315 \\
y &= -75\sqrt 2 \end{align}
(Working on Vector $\underline A$)
\begin{align}x = |A|\cos \theta \\
x = 200\cos 60 \\
x = 100 \end{align}
\begin{align}y &= |A|\sin \theta \\
y &= 200\sin 60 \\
y &= -173.21 \text{(2 decimals)} \end{align}
$\underline B  - \underline A  = 75\sqrt 2\underline i - 75\sqrt 2\underline j + -(100\underline i + 173.21\underline j)$ 
$\underline B  - \underline A  = 6.066\underline i - 279.28\underline j$
 [/INST] $$ \vec{200} =(200\cos(60))i + (200\sin(60))j=100i+100\sqrt3j$$
$$ \vec{150} = (150\cos(45))i-(150\sin(45))j=75\sqrt{2}i-75\sqrt{2}j$$
$$ R= \vec{200} + \vec{150} =?$$
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