For what value of "a" the line and the plane are parallel in real coordinate space?

Question

The question that I am facing is the following:

"For which choice of a real number $a$ are the line $x = y-1 = \frac{(z+1)}{2}$ and the plane $ax+y+2z=3$ in $\mathbb{R}^{3}$ parallel?

a) $a=-5$

b) $a=0$

c) $a=1$

d) Nothing of the above"

I tried finding the dot product of the direction vector of the line and the normal vector of the plane, but I am unsure about how to get to the vector of the line, and how to reorder its equation with the two equalities.

Thank you in advance for any help or guidance!

Answer 1

Hint: the direction vector of line is $\vec{s}=\{1, 1, 2\}$.