# Thread: Two 3-D Line questions.

1. ## Two 3-D Line questions.

Just give the trick and the final answer.It will do.

1.Find the equations of the line of intersection of the two planes
x-2y+3z=4
2x-3y+4z=5

2.Find the equations of the line passing through (1,1,1)and parallel to the plane 2x+3y+z+5=0

2. Originally Posted by prohank
1.Find the equations of the line of intersection of the two planes
x-2y+3z=4
2x-3y+4z=5
The direction of the line is $\displaystyle <1,-2,3>\times <2,-3,4>$.
Now you need to find a point, any point, on both planes.

3. And how do i find that point?

4. Originally Posted by prohank
And how do i find that point?
Find $\displaystyle (x,y,0)$ so that it is on both planes.

5. Can you show me how should i do that.Sorry! but I really don't know.

6. Originally Posted by prohank
Can you show me how should i do that.Sorry! but I really don't know.

7. Originally Posted by prohank
Can you show me how should i do that.Sorry! but I really don't know.
If you're studying at this level you are not expected to be this helpless. Post #4 told you what to do! Did you try doing it. What did you get? Where are you stuck?

8. Originally Posted by prohank
Just give the trick and the final answer.It will do.

1.Find the equations of the line of intersection of the two planes
x-2y+3z=4
2x-3y+4z=5

2.Find the equations of the line passing through (1,1,1)and parallel to the plane 2x+3y+z+5=0
there is no "trick" only understanding. the point is not to get "the answer" but to be ABLE to get the answer.

on your 1st problem, you have 2 planes: 2 equations with 3 variables. you should be able to reduce this to one equation with 2 variables.

9. Another way to solve (1)
x-2y+3z=4
2x-3y+4z=5

are two equations in three unkowns. You can solve for two of them in terms of the third- for example, you can eliminate y by multiplying the first equation by 3, the second equation by 2 and then subtracting. Solve the resulting equation for z in terms of x. Then put that back into either equation so you have and equation in x and y only. Solve that equation for y in terms of x. Then you have x= t, y= f(t), z= g(t) as parametric equations for the line.

As for "2. Find the equations of the line passing through (1,1,1)and parallel to the plane 2x+3y+z+5=0", it makes no sense. There are an infinite number of such lines. There is an entire plane containing (1,1,1) and parallel to the given plane. Any line in that plane is a solution to this problem.

10. Yeaa I found that point
I got the points as -1/2,0,3/2
But they don't match the answer.
So I thought of asking if I could get any help
2(x+2)=y+3=2z.
Thanks all.

11. it would be helpful if you showed HOW you got the answer.

12. Actually I used a different method.
Plane1 + (lambda)Plane2
brought it in the form of
(a+blambda ) + etc
and then substituted the points -1/2,0,3/2 in it
I found lambda which is 4/5
and then got the eqn as
13x-22y+31z.