core pure 1 vectors question help!!

i need help with reflecting a point in a line. i’m trying to use the method with the hint in the question, but i don’t understand how i find the line segment containing p and reflected point of p’s direction vector…
my working out only consists of a dot product between the given line’s direction vector and x, y, z the segment’s direction vector..
https://imgur.com/a/XpiMF6g

A sketch helps and it would help to see your working but if the line is
a + lambda*d
so a is the point on the line and d is the direction and p is the point to be reflected, then pm will be perpendicular to d and the reflection is twice that added to p. So m is a point on the line (value of lambda) and pm is perpendicular to d (zero dot product).

thank you this makes much more sense!! to clarify to find pm you would just minus the general point on the line as m is on the line, from p. then for the value of lambda found after dot product, twice that value is the reflected point of p..
(sorry if i don’t make sense…)