Equation of vector pass thru point

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Homework Help Overview

The discussion revolves around understanding the positioning of a point relative to two planes in a three-dimensional space, specifically focusing on the geometric interpretation and the equations governing the planes.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to clarify the location of point A in relation to the planes, questioning whether it can be considered outside or on the planes based on its coordinates.

Discussion Status

Some participants have provided guidance on checking the coordinates of point A against the equations of the planes to determine its position. There is an ongoing exploration of the implications of these checks, with no explicit consensus reached on the interpretation of the results.

Contextual Notes

Participants are working with specific equations of the planes and the coordinates of point A, which are critical to the discussion but may not be fully understood by all. The need for clearer diagrams has also been expressed, indicating potential challenges in visualizing the problem.

kelvin macks
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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


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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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