Vectors (planes and perpendicular vectors) Watch

BobbyBigMaths
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A line m lies in the plane p and is perpendicular to l. The line m passes through the point with
coordinates 5, 3, 1. Find a vector equation for m.(Direction Vector for l = 2i+j+3k and equation of plane is 2x -y -z = 6 This is question 7 from 9709/32 FM 2016 I managed to solve it with both the dot product and the cross product but I have an issue with the wording in the question. If the line is contained within the plan and l is perpendicular to it how is it that l is not parallel to the normal vector of the plane? If I could get an explanation of the wording that would be nice Thanks!
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RDKGames
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(Original post by BobbyBigMaths)
A line m lies in the plane p and is perpendicular to l. The line m passes through the point with
coordinates 5, 3, 1. Find a vector equation for m.(Direction Vector for l = 2i+j+3k and equation of plane is 2x -y -z = 6 This is question 7 from 9709/32 FM 2016 I managed to solve it with both the dot product and the cross product but I have an issue with the wording in the question. If the line is contained within the plan and l is perpendicular to it how is it that l is not parallel to the normal vector of the plane? If I could get an explanation of the wording that would be nice Thanks!
Why would it necessarily be parallel to the normal? Below are two scenarios where l is not parallel to the normal. In fact, there are infinitely many scenarios where l is perpendicular to m and not parallel to normal, and only ONE in which l is perp. to m and parallel to normal. 3D visualisation is essential here but hopefully the images help convery what I mean.

Also, it is obvious that l in your question is not parallel to the normal because the normal has direction vector (2,-1,-1) which is not a multiple of (2,1,3).

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BobbyBigMaths
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Oh damn, my bad but thanks a lot I see my mistake now
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