Not Sure Where To Go From Here (intersections of lines, of planes)

[Umbra]

I'm stuck on 14 and not sure where to go from here. I was also wondering if 15 was correct?
Thanks!

 

[Harry_the_cat]

I'm stuck on 14 and not sure where to go from here. I was also wondering if 15 was correct?
Thanks!

In Q14 you have 3 equations with 3 unknowns [1], [2] and [3].

Solve for [1] and [2] simultaneously, and then check solution in equation [3].

Rearrange [1] to get s = -3t - 2.

[3] is s = -1 + t

So -3t - 2 = -1 + t etc.....

 

[Umbra]

In Q14 you have 3 equations with 3 unknowns [1], [2] and [3].

Solve for [1] and [2] simultaneously, and then check solution in equation [3].

Rearrange [1] to get s = -3t - 2.

[3] is s = -1 + t

So -3t - 2 = -1 + t etc.....

Thank you! That makes more sense then what I was thinking I had to do.

 

[Umbra]

In Q14 you have 3 equations with 3 unknowns [1], [2] and [3].

Solve for [1] and [2] simultaneously, and then check solution in equation [3].

Rearrange [1] to get s = -3t - 2.

[3] is s = -1 + t

So -3t - 2 = -1 + t etc.....

Here is my new answer. Does that mean -1 = -8.75 is the intersection? Or did I mess up somewhere?

 

[pka]

Here is my new answer. Does that mean -1 = -8.75 is the intersection? Or did I mess up somewhere?

Are these two lines skew lines?

 

[Umbra]

Are these two lines skew lines?

I'm not sure. I was thinking that when I saw the answer, but the question wants me to find the intersection so I feel as though I did something wrong.

 

[pka]

I'm not sure. I was thinking that when I saw the answer, but the question wants me to find the intersection so I feel as though I did something wrong.

\(\displaystyle \begin{align*}6+3t&=4-s \\-1+t&=s\\-4t&=5+5s \end{align*}\)

Now unless you can find values of \(\displaystyle s~\&~t \) which satisfy each of those equations at the same time, then the lines are skew lines.

 

[Umbra]

\(\displaystyle \begin{align*}6+3t&=4-s \\-1+t&=s\\-4t&=5+5s \end{align*}\)

Now unless you can find values of \(\displaystyle s~\&~t \) which satisfy each of those equations at the same time, then the lines are skew lines.

I'm going to have to say they are skew lines then unless I made a mistake somewhere. Interesting, but helpful. Thank you, pka.
Edit: I'm dumb, I just did it for x and they matched.