Vectorial Algebra: Parallel, Perpendicular or Neither?

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The discussion centers on determining the relationship between a line defined by point P=(1,-1,1) and direction vector d=[2,3,-1], and the plane given by the equation 2x+3y-z=1. The normal vector of the plane is identified, which is crucial for assessing whether the line is parallel, perpendicular, or neither. The point P is noted to be independent of the direction vector d, leading to confusion about how to relate them. The use of dot and cross products is suggested for evaluating the relationships, but the poster expresses uncertainty about the relevance of the question to physics, suggesting it may be more appropriate for a math forum. Ultimately, the discussion highlights the need for clarification on the mathematical concepts involved in the problem.
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Homework Statement


The line l passes through the point P=(1,-1,1) and has direction vector d=[2,3,-1]. Determine whether l and P are parallel, perpendicular, or neither to 2x+3y-z=1.


Homework Equations



n.x=n.p, also cross product for parallel lines, and dot product for perpendicular.

The Attempt at a Solution


I don't know how to relate the point, P, to the directional vector,d. I am pretty sure that I can do the rest.
 
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P isn't related to d, they are independent. 2x+3y-z=1 is a plane. What it's normal vector? Question like this probably don't belong in Physics. I'd put them in a math HW forum.
 
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