The line $l_1$ has the equation $r=(6i+2−2k)+λ(4i+5j−k)$ and the plane $π_1: 2x−y+4z=4$, the line $l_2$ is the reflection of $l_1$ in the plane π1. Find the exact vector equation of line $l_2$
So the line intersects the plane when $λ=−2$, giving the point $(−2,−8,0)$ which will be common on $l_1$ and $l_2$. I have managed to get a direction vector of $(92/21i + 206/21j +26/21k)$ but I don't think this is right. Any help would be appreciated.