Vector parallel to a plane 3x+2z=3

Question

I have a plane whose equation is $3x+2z=3$

My question is, is vector: $(0,1,0)$ parallel to the plane? Or how do I determine if a vector is parallel to a certain plane?

Answer 1

A normal to your plane comes from the coefficients of $x,y,z$ i.e. $(3,0,2)$.

If $(0,1,0)$ is parallel to the plane, then it is perpendicular to the normal, which you can check with the dot product.

Answer 2

Compute the CrossProduct $$[3,0,2]\times [0,1,0]$$