vectors help urgent please ;((

someone pls help me with part(iii) using the ratio method, do include your detailed explanations thanks alot my a2 is in weeks
answer & question are attached below.
ps i could get the 2 equations, i am just having problem with the ratio part thanks alot

So you are looking for a direction vector that lies in p (so is perpendicular to the normal to the plane) and is also perpendicular to the direction of the line. Is there a vector operation that takes two vectors and gives a new vector that is perpendicular to both of them?

yeap, im looking for the directional vector. the mark scheme says we can use the ratio method to get (6,2,-1) but im not too sure how do you have any idea?