Find the coordinates of a point where a line intersects the y-axis.

[vparikh]

Homework Statement

The following equation describes a straight line:
⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩
Find the coordinates of the point where this line intersects the y-axis.

Homework Equations

Equation of a Line: r = r_o + tv

The Attempt at a Solution

I'm not really sure how y-intercepts work in 3d and I'm having trouble even attempting a solution. My guess was the r_o point <-1,0,-2> because the y coordinate is zero but I don't think that it would be that easy. Also, this is my first time posting a question on the Physics Forum site so please go easy on me if I messed anything up :)

 

[Dick]

Homework Statement

The following equation describes a straight line:
⟨x, y, z⟩ = ⟨−1, 0, −2⟩ + t⟨1, 2, 2⟩
Find the coordinates of the point where this line intersects the y-axis.

Homework Equations

Equation of a Line: r = r_o + tv

The Attempt at a Solution

I'm not really sure how y-intercepts work in 3d and I'm having trouble even attempting a solution. My guess was the r_o point <-1,0,-2> because the y coordinate is zero but I don't think that it would be that easy. Also, this is my first time posting a question on the Physics Forum site so please go easy on me if I messed anything up :)

It's almost that easy. <-1,0,-2> is in the x-z plane, it isn't on the y-axis. A point on the y-axis looks like <0,y,0>.

 

[vparikh]

So then it has to be the point when the x and z coordinates are zero?

 

[Dick]

So then it has to be the point when the x and z coordinates are zero?

Yes. What is it?

 

[vparikh]

Well the equation multiplied out would be

<t-1,2t,2t-2>

so to make the x and z zero, x has to be 1 and y has to be 1.

So would <1,1,1> be a point that this line intersects the y axis?

 

[Dick]

Well the equation multiplied out would be

<t-1,2t,2t-2>

so to make the x and z zero, x has to be 1 and y has to be 1.

So would <1,1,1> be a point that this line intersects the y axis?

Not quite sure what you are thinking there. I would say to put x=0 you should pick t=1.

 

[vparikh]

Okay, so where t=1 the coordinates are <0,0,0> and thus intersect the y-axis at that point?

 

[vparikh]

Wait, no it would be <0,2,0>

 

[Dick]

Okay, so where t=1 the coordinates are <0,0,0> and thus intersect the y-axis at that point?

?Can you explain how putting t=1 into <t-1,2t,2t-2> gives you <0,0,0>?

 

[vparikh]

?Can you explain how putting t=1 into <t-1,2t,2t-2> gives you <0,0,0>?

Sorry, bad algebra. <0,2,0>

 

[Dick]

Sorry, bad algebra.

Ok. Yes, it's <0,2,0>.

 

[vparikh]

Ok. Yes, it's <0,2,0>.

Thanks for the help, I really appreciate it!