Answer
$\vec A=(-49.9m)\hat x$
$\vec B=(1.5m)\hat x$
Work Step by Step
We can find the required vectors as follows:
$\vec A+\vec B+\vec C+(\vec A-\vec B)+(-\vec C)=(13.8)m\hat x+(-51.4m)\hat x+(-62.2m)\hat x$
$\implies 2\vec A=(-99.8m)\hat x$
$\implies \vec A=(-49.9m)\hat x$
Now we can find the vector B as
$\vec A-\vec B=(-51.4m)\hat x$
$(-49.9m)\hat x-\vec B=(-51.4m)\hat x$
$\vec B=(1.5m)\hat x$
