Vector perpendicular to the plane

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Homework Help Overview

The discussion revolves around determining the value of 'a' for which the vector v=(-2,1,a) is perpendicular to the plane defined by the equation z=6x-3y+4. The subject area involves vector mathematics and geometric interpretations of planes and normals.

Discussion Character

  • Conceptual clarification, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to relate the vector to the plane's normal vector and checks proportionality of their components. Other participants question the accuracy of the normal vector's components and explore the use of the dot product to establish perpendicularity.

Discussion Status

The discussion is active, with participants identifying potential errors in the original poster's understanding of the normal vector. There is a suggestion to use the dot product as an alternative method to verify perpendicularity, indicating a productive exploration of different approaches.

Contextual Notes

Participants are navigating discrepancies between textbook solutions and their own calculations, which may influence their understanding of the problem setup.

xstetsonx
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For what value of a is the vector v=(-2,1,a) perpendicular to the plane z=6x-3y+4?

i looked the book and my teacher's solution they are different so i just want to make sure i did this right...


Vector v is perpendicular to the plane if it is parallel to the plane’s normal vector. A vector which is normal (= perpendicular) to the plane is n=(6,-3, 4) Hence, v parallel n if their coordinates are proportional, i.e. −2/6=1/3=a/4, therefore a=4/3



can someone correct me if i am wrong?PLZ
 
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You got one component of the normal vector wrong.
 
how? z=6x-3y+4 don't u just take the coefficient and that is your normal vector?
 
Do you see a 4z in your equation?
 
aw crap so is it -1 then?
 
Last edited:
since i have two vectors why can't i do Vector1 . Vector2=0?
since the dot product says a.b=0 is perpendicular to each other?
 

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