Question

Normal form problem [see attachment]

Answer 1

I'm not familiar with the notation but I'll guess this refers to the equation:

$p = x \cos \phi + y \sin \phi$

$11\pi/6$ is -30 degrees

$4 \sqrt{3} = x (\sqrt{3}/2) - y/2$

$\sqrt{3} x - y - 8 \sqrt{3} = 0$

Choice b