# vectors

The line l1 has vector equation r = (2, -1, 2) + lambda(4, -3, 4) The plane pi has equation r dot (1, -1, -1) =4.

The line l2 is the reflection of line l1 in the plane pi
Find a vector equation of the line l2

I've managed to find what M is and checked this against the mark scheme, but am unsure where (4, -3, 0) comes from and can't seem to end up with a direction vector in the same ratio as the answer

Mark scheme (Q 12): https://www.activeteachonline.com/default/player/document/id/721195/external/0/uid/357726
Original post by Amy.fallowfield
The line l1 has vector equation r = (2, -1, 2) + lambda(4, -3, 4) The plane pi has equation r dot (1, -1, -1) =4.

The line l2 is the reflection of line l1 in the plane pi
Find a vector equation of the line l2

I've managed to find what M is and checked this against the mark scheme, but am unsure where (4, -3, 0) comes from and can't seem to end up with a direction vector in the same ratio as the answer

Mark scheme (Q 12): https://www.activeteachonline.com/default/player/document/id/721195/external/0/uid/357726

I only see q1 and q2. Just screenshot what you are looking at and post that.
Original post by RDKGames
I only see q1 and q2. Just screenshot what you are looking at and post that.

Question:
Mark scheme:
They chose an arbitrary point on l1, so why not lambda=0, then used a similar method to get its reflection which gives the given point, then you have two points on the reflected line ...
Original post by Amy.fallowfield
Question:
Mark scheme:
(edited 1 month ago)
Original post by mqb2766
They chose an arbitrary point on l1, so why not lambda=0, then used a similar method to get its reflection which gives the given point, then you have two points on the reflected line ...

Oh ok. Thank you
Original post by Amy.fallowfield
Oh ok. Thank you

Note another way would be to take dot product of l1s direction vector with the unit normal vector, then subtract twice that from the direction vector to get its reflection.
Original post by mqb2766
Note another way would be to take dot product of l1s direction vector with the unit normal vector, then subtract twice that from the direction vector to get its reflection.

Fwiw, if n is the non-normalised normal vector you can skip the normalisation and instead subtract 2(v.n)/(n.n)
Original post by DFranklin
Fwiw, if n is the non-normalised normal vector you can skip the normalisation and instead subtract 2(v.n)/(n.n)

Agreed, you just need to do that division at some point.