Straightforward vector calc problem

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Homework Help Overview

The discussion revolves around a vector calculus problem involving the calculation of the distance from a point to a plane. The original poster is seeking clarification on the projection method needed to solve the problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to understand how to use projections with vectors, specifically mentioning the normal vector to the plane and seeking guidance on identifying the second vector needed for the projection.

Discussion Status

Participants are engaging in a constructive dialogue, with one suggesting the use of a geometric approach by visualizing the problem and considering the projection of a vector from the point to the plane. The original poster indicates a moment of clarity following this input.

Contextual Notes

The original poster expresses uncertainty about the relevant equations and methods for finding the distance, indicating a need for foundational understanding in vector projections and their application to this problem.

tjaeger
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Studying for finals and I don't recall how to do projection and I don't like the explanation my textbook gives

Problem: Find the distance from the point (1,3,-2) to the plane 2x + y - z = 1

The answer to this problem should be sqrt(6)

Relevant equations: ?

The attempt at a solution:

I know I have to do a projection of using two vectors, and I know one of the vectors is the normal vector to the plane (2i + j + k). I'm not sure how to find the other vector using the point given and which of the vectors is projected onto the other.
 
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Well, what equation / method are you using to find the distance from the point to the plane?
 
draw a picture first...
consider an arbitrary point P on the plane, let Q=(1,3,-2)
now the magnitude of the proj of PQ in the direction of your normal vector IS the distance from Q to plane...
 
ok, thanks. I got it now.
 

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