# Help needed with 3d geometry problem: important

• elphin
In summary, the problem is that the equations are unsolvable. You need to find a different way to solve it.
elphin
help needed with 3d geometry problem: important!

## Homework Statement

find the equations of the two planes through the origin which are parallel to the line
(x - 1)/2 = (-y-3) = (-z-1)/2
and at a distance of 5/3 from it. also, show that the planes are perpendicular

## The Attempt at a Solution

my attempt at the solution

plane equations passing through (0,0,0) are ax+by+cz=0 (&) a'x+b'y+c'z=0
now, 2.a - b - 2.c = 0 (since direction ratios of given line is perpendicular to the normal of the plane)
also by distance formula (a.(1) + b.(-3) +c.(-1))/(a^2 + b^2 + c^2)^(1/2) = 5/3
the a - 3.b - c = 5/3 (since a^2 + b^2 + c^2 = 1)
and now i am stuck...

FYI : [the answer is 2x+2y+z=0; x-2y+2z=0]

You have got the equations you need to find the normals. 2*a-b-2*c=0, a-3*b-c=5/3 and a^2+b^2+c^2=1. If you solve those will get normals for the two planes. The books answer doesn't assume a^2+b^2+c^2=1 so be prepared to multiply the normal by a constant to get the books answers.

the problem is the equations are unsolvable

2*a - b - 2*c = 0
the we get (a - c) = b/2
substitute this in a - 3*b - c =5/3
we get b = -2/3
now substitute b = -2/3 in a^2 + b^2 + c^2 = 1
we get a^2 + c^2 = -1/3 !

elphin said:
the problem is the equations are unsolvable

2*a - b - 2*c = 0
the we get (a - c) = b/2
substitute this in a - 3*b - c =5/3
we get b = -2/3
now substitute b = -2/3 in a^2 + b^2 + c^2 = 1
we get a^2 + c^2 = -1/3 !

No, you don't get this. You should get a^2 + c^2 = 1 - (2/3)^2 = 5/9.

RGV

ooops .. sorry .. you are right ..

let me sum up this situation in an equation...

sleepless night + math => (2/3)^2 = (4/3)

thanks dude...

## 1. What is the problem about?

The problem involves a 3D geometry concept that requires assistance from someone knowledgeable in the subject.

## 2. What is the importance of this problem?

This problem may be important for understanding a particular concept or for completing a larger project or assignment. It is important to seek help in order to fully understand and solve the problem.

## 3. What specific help is needed with this 3D geometry problem?

Specifically, help is needed in understanding the concepts involved and in finding the correct approach or solution to the problem.

## 4. Are there any resources available to assist with this type of problem?

Yes, there are many online resources and textbooks that can provide additional explanations and examples for 3D geometry problems. It may also be helpful to seek assistance from a tutor or classmate.

## 5. What is the best way to approach this type of problem?

The best way to approach a 3D geometry problem is to break it down into smaller, more manageable steps and to use diagrams or visual aids to better understand the problem. It may also be helpful to review any relevant formulas or concepts before attempting to solve the problem.

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