Shortest distance between two skew lines with Y13 FM in #MathsToday (yesterday) so time to crack out this lovely proof! Nice link to volume as the formula is scalar triple product divided by cross product; volume of parallelopiped divided by area of parallelogram = height. #ALevelMaths - ThreadSky

mrsouthernmaths.bsky.social • 84 days ago

Shortest distance between two skew lines with Y13 FM in #MathsToday (yesterday) so time to crack out this lovely proof!

Nice link to volume as the formula is scalar triple product divided by cross product; volume of parallelopiped divided by area of parallelogram = height.

#ALevelMaths

Comments

rufuswilliam.bsky.social•83 days ago

📌

mrconnormaths.bsky.social•84 days ago

📌

mathforge.org•84 days ago

How did/do you explain that link?

mrsouthernmaths.bsky.social•83 days ago

So one of the approaches we used to find the distance between two skew lines was to consider two parallel planes containing each line respectively. The shortest distance between these planes would be the shortest distance between the lines and we did this using the formula for shortest distance

mrsouthernmaths.bsky.social•83 days ago

from a point to a plane.

If we were to draw a parallelogram in each plane such that they "lined up", you could create a parallelapiped. The scalar triple product would find its volume, as would multiplying the area of the parallelogram (cross product) by the distance between the planes.

mathforge.org•83 days ago

And did you point this out to the students, or was it one of those that as a teacher you notice and appreciate but it would overcrowd the story for students?

mrsouthernmaths.bsky.social•83 days ago

I pointed it out, using 2 A3 whiteboards as props!

tcorica.bsky.social•83 days ago

I approach it this way: we want a plane thru L1 that's // to L2. Imagine sliding L1 (keeping parallel to orig L1) toward L2 until they intersect. The plane containing the two intersecting lines has n = v1×v2. We then do dist. from any pt on L1 to the plane. Desmos3d:
https://www.desmos.com/3d/dzkvrfwp1x

tcorica.bsky.social•83 days ago

Really like the geometric interpretation. I've only used that in the past for distance from point to line (area of //ogram divided by base is height), so this is a nice extension of that!

suffolkmaths.bsky.social•83 days ago

Very nice
Unimportant but your PQ vector is QP 🙂

mrsouthernmaths.bsky.social•82 days ago

Good spot!

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