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


The point of intersection of the line with the yz plane is the same for both the lines L and L'.
The point of intersection is  $(0,-6/5,16/5)$ .
$L={x-1\over -5}={y+2\over 4}={z-3\over 1}$
Now after reflection the slope of the line will change. The inclination with the x axis will reverse but that of the y and z axis will remain same. You can see that. 
$L'={x-0\over 5} = {y+6/5\over 4} = {z-16/5\over 1}$
