Obtaining Directions Vector for Perpendicular Lines

[Miike012]

Refer to paint document for question

The questions says that the line is parallel to plane x + y + z = 2 and perpendicular to the line x = 1 + t, y = 1 -t, z = 2t

My question is if the line is parallel to the plane it must be perpindicular to the planes normal, right? If this is true shouldn't the vector representation of the line x = 1 + t, y = 1 -t, z = 2t which is <1,-1,2> be parallel to the planes normal?

 

[Simon Bridge]

My question is if the line is parallel to the plane it must be perpindicular to the planes normal, right? If this is true shouldn't the vector representation of the line x = 1 + t, y = 1 -t, z = 2t which is <1,-1,2> be parallel to the planes normal?

No. Something you can see with a model - use a sheet of paper to represent the plane, draw a line on the sheet - that line is parallel to the plane right? Now use your pen to represent another line ... place the pen so it is perpendicular to the line in the paper.

Your initial impulse will be to put the pen perpendicular to the paper - well done - however, see if you can put it at slant to the paper and still keep it perpendicular to the line in the paper.