Equation of a Plane Passing Through Two Parallel Lines (2-3t, -t, 1+2t) and (3s, 4+s, 5-2s)

How do we find an equation of the plane passing through two parallel lines?
The two lines are (2-3t, -t, 1+2t) and (3s, 4+s, 5-2s).
In general, when we want to find an equation of a plane, we need to know a point lying in the plane, and the normal vector of the plane (which is perpendicular to the plane). So, we first need to obtain three points from the two lines (and make sure they are NOT collinear) so that we can find the normal vector!
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[@uaultda7458]

Hey man! I am Brazilian and I was having a very hard time trying to discover how to do this... Thankfully I found out your video! Thank you so much!

[@GlassofNumbers]

That's good! Check out my other videos about finding equations of planes. And share my videos with your friends 😁

[@sgeddegs]

dude, you're a godsend, thanks so much for this video

[@GlassofNumbers]

Thank you!! Please share my videos to others 😁

[@hamdansiddiqui3294]

God bless you bro far better than my teacher explanation of these

[@GlassofNumbers]

Thank you! I am glad you like my explanation! Please share my videos 😁

[@andreacerulli9669]

I love this channel 💖 thanks for everything
Greetings from Mexico 🇲🇽

[@GlassofNumbers]

Thank you Andrea! I am glad that the videos help! Please share my videos to others who you think may need them! 😃

[@mrb03mrb]

Thank you this was so great!

[@GlassofNumbers]

Thank you! Please share this video with others 😁👍

[@georgeshao]

tysm, this was so helpful

[@GlassofNumbers]

Good to hear my video helps! Please share my videos to others 😁

[@user-dq8zq8pk9t]

thanks

[@GlassofNumbers]

No problem! Glad you like my video! Please share it with others 😁

[@yoshansameera6460]

Why did u use as t=0,t=1

[@GlassofNumbers]

You can choose other values for t. But the calculation for t=0 and t=1 is easier. 😁

[@memoryfiles8768]

[@GlassofNumbers]

Thank you! Glad you like my videos!

[@JustAGamer70]

I got 0 for i,j,k. Why could this be?

[@GlassofNumbers]

You meant for the normal vector of the plane?

[@buongiorno5233]

This happened to me in my Calc 3 midterm a couple hours ago :). The cross product of two parallel vectors is 0, that might be why.