Find an equation of the plane containing $(1,0,0)$ and the line $⟨1,0,2⟩+t⟨3,2,1⟩$

Question

Find an equation of the plane containing $(1,0,0)$ and the line $⟨1,0,2⟩+t⟨3,2,1⟩$

I know the equation of a plane is $ax+by+cz=d$ and so I need to find a normal vector or $<a,b,c>$ (I think), which I believe would be $<3,2,1>$

After that I thought I use the point $(1,0,0)$ to form $a(x-x_0)+b(y-y_0)+c(z-z_0)$ but I can't seem to get the right answer. Help!

Answer 1

Hint: Let $A=(1,0,0)$, $B=(1,0,2)$ and $\vec u=(3,2,1)$. Consider the cross product $\overrightarrow{AB}\wedge \vec u$.