Is the line parallel to the plane?

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Homework Help Overview

The discussion revolves around determining whether a given line is parallel to a specified plane in three-dimensional space. The subject area involves vector analysis and geometric interpretation of lines and planes.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use the dot product of the line's directional vector and the plane's normal vector to assess parallelism. Some participants question the correctness of this approach and suggest additional considerations regarding intersection.

Discussion Status

Some guidance has been offered regarding the relationship between parallel lines and normal vectors, indicating a productive direction. Multiple interpretations of the line's relationship with the plane are being explored, particularly concerning intersection points.

Contextual Notes

The original poster has provided a link to their working for review, indicating a desire for feedback on their calculations. There is an implication of homework constraints, as the discussion is framed within a homework help context.

cyt91
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Is the line x=1-2t,y=2+5t,z=-3t parallel to the plane 2x+y-z=8?

I've used the approach of finding the dot product of the directional vector of the line and the vector normal to the plane in this question. The line is not parallel to the plane.
But I'm not too sure if my working is correct. Can anyone please check my working?

It's here:

https://skydrive.live.com/?cid=6b04...751C72E14AD&id=6B041751C72E14AD!160&sc=photos

Thank you.
 
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It is correct. But you need to write a sentence for explanation, that if it was parallel with the plane than it would be perpendicular to the normal vector of the plane.

ehild
 
Ok. Thanks.
 
Also, if the line were not parallel to the plane, it would intersect the plane at some point in the plane. Does it?
 

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