Suppose that the line $\ell$ is represented by $\mathbf{r}(t) = \langle 15+4 t, 17+6 t, 21+ 8 t \rangle$ and the plane $P$ is represented by $2x+4y+5z = 23.$

---

1. Find the intersection of the line $\ell$ and the plane $P.$ Write your answer as a point $(a,b,c)$ where $a$, $b$, and $c$ are numbers.
Answer:

2. Find the cosine of the angle $\theta$ between the line $\ell$ and the normal vector of the plane $P$.
Answer: $\cos \theta =$

---

Note: If there is no intersection, write "none" for both answers.