Reflection of a Light Ray I found this problem to be very hard while studying for the exam: 

Let
  $$L: \vec r(t)=<1,-2,3>+t<-5,4,1>, \qquad t \in \mathbb{R}$$
  be a line. Light is traveling along the line $L$ in the direction of increasing $t$ value. Let $\Omega: x=0$ (the $yz$ plane) be a mirror. Find the vector equation of the line $\hat L$ that is the reflection of line $L$ by $\Omega$ 
  Any help would be helpful!

Any help would be helpful!

My solution 
  $$L: \vec r(t)= 1/5<0,-6,16>+t<5,4,1>, \qquad t \in \mathbb{R}$$


Perhaps I’ve misunderstood something in the problem statement, but this seems rather straightforward. The problem talks about lines, not rays, so the point at which the given line intersects the mirror isn’t directly relevant.  
Forget about the line for the moment. What is the image of an arbitrary vector $\langle x,y,z \rangle$ when reflected in the $yz$-plane? It is simply $\langle -x,y,z \rangle$. To find the equation of the line’s reflection, apply this same transformation to the given equation, resulting in the line $$\langle -1,-2,3\rangle + t\langle 5,4,1\rangle.$$   
Now, if indeed you’re really supposed to find the incident and reflected rays, then you do need to reparametrize by finding where the line intersects the reflective plane (which is also the point of intersection of the two lines), but it seems to me that you then also have to specify that $t\ge 0$ so that you get a ray rather than a line.
