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Multivariable Calculus

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Find the Intersection of Two Planes

MVCALC-OLAG14

Let $A$ be a plane with normal vector $\langle 1,1,1 \rangle$ that contains the point $(2,0,1)$.

Let $B$ be a plane with normal vector $\langle 1,0,1 \rangle$ that contains the point $(3,1,0)$.

Let $L$ be the line of intersection of $A$ and $B$. In a set of parametric equations for $L$, we have:

$$x=3t$$
$$y=0$$
$$z=-ct+c$$

What is the value of $c$?