Equation of vector pass thru point

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The discussion focuses on understanding the position of point A in relation to two planes defined by their equations. A participant requests a clearer diagram for parts c and d of a homework problem, expressing confusion over the provided diagram. Another participant confirms that point A is outside both planes by substituting its coordinates into the plane equations, demonstrating that they do not satisfy either equation. This confirms that point A does not lie on either plane, clarifying the initial confusion. The conversation emphasizes the importance of verifying point positions through mathematical substitution.
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Homework Statement




can someone draw me a better diagram for part c and d ? i can't understand the diagram given . This is the suggested ans form my book


Homework Equations





The Attempt at a Solution

 

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kelvin macks said:

Homework Statement




can someone draw me a better diagram for part c and d ? i can't understand the diagram given . This is the suggested ans form my book

Here you are. A is outside both planes. P is point of the intersection line l

ehild
 

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how do u know that point a is located outside? why point a can't be on the plane?
 
Plug in the coordinates of A into the equations of both planes. Does it fit?

ehild
 
ya , the ans is correct . why? i can't understand
 
A: x=1, y=0, z=1. A is in the plane π1 if its coordinates fulfil the equation of the plane.

Plane π1: x-y+2z=1. Plugging in he coordinates of A: 1-0+2 =3≠1
Plane π2: 2x+y-z=0. Plugging in he coordinates of A: 2-1=1≠0

A is not point of any of the planes.

ehild
 
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