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## Homework Statement

Given a common intersection point (3,4,5), find 3 different planes.

## Homework Equations

None

## The Attempt at a Solution

What I did is let

a

_{1}x+a

_{2}y+a

_{3}z=a

b

_{1}x+b

_{2}y+b

_{3}z=b

c

_{1}x+c

_{2}y+c

_{3}z=c

3=D

_{x}/D 4=D

_{y}/D 5=D

_{z}/D

I set D=2, therefore D

_{x}=6 D

_{y}=8 D

_{z}=10,

I was stuck then, no matter how I did I just got a bunch of unknown.

This question is supposed to find any 3 linear equations(aka 3 planes) that satisfy the intersection point.

Well, who doesn't know how to find the intersecting point using Cramer's rule...

P/S: This question comes up in my calculus 3 question, and I have not taken any algebra course yet, so I only know the condition for Cramer's rule for a common intersection point to take place which is D not equal to 0.