Vectors

[haughty prism]

.

[warm elm]

yo

do you still need help

[haughty prism]

Yes @warm elm

Sorry I was sleeping

😭

[warm elm]

its nw

so this question looks very not fun

[haughty prism]

😂😂

[warm elm]

part a yeah

[haughty prism]

Yup

[warm elm]

ok so i might ask first

if i give you a line and a point

how would you describe the shortest distance from that point to the line

what nice property does it have

[haughty prism]

It is perpendicular right ?

[warm elm]

it is

so if you have two lines

and you want the shortest distance between them

what nice property do you think this shortest distance will have

[haughty prism]

Hmm

As in, in vectors ?

[warm elm]

it has a nice property

i want you to describe it

[haughty prism]

Like a • b = 0?

[warm elm]

(hint: think about fixing a point on one line, and shortest distance from that point to the other line)

[haughty prism]

I actually don't know

I see it

[warm elm]

so your shortest distance between the two lines

will actually be

[haughty prism]

Maybe like a right triangle

[warm elm]

perpendicular to both lines

[haughty prism]

Yes that's true

[warm elm]

ok so

i think you know but

how do you check for perependicular

with vectors

[haughty prism]

a • b = 0

[warm elm]

awesome so

lets say we want the line that has the shortest distance from one line to the other

like that shortest distance we want the line its on

and since we dont know anything yet lets just say its components are

(a, b, c)

[haughty prism]

This is the shortest line that you are describing right?

[warm elm]

yeah

[haughty prism]

Ok I'm with you

[warm elm]

ok so

(a, b, c) is apparently perpendicular to

both l1 and l2

so can you maybe setup some equations?

[haughty prism]

Let me see

One second

[warm elm]

actually this is really really gross

[haughty prism]

I don't get it because the a and b are supposed to be direction vectors

Yes it doesent make sense

If I could find the marks scheme

Could you look at it and explain it to me

Possibly

[warm elm]

i can try

[haughty prism]

Ok give me one sec

[warm elm]

so that second bit

thats trying to find the vector thats perpendicular to both lines

or at least some multiple of it

[haughty prism]

I don't even understand the mark scheme tbf

[warm elm]

oh formula for shortest distance

do you have a formula booklet by any chance

[haughty prism]

One second

Not that helpful I don't think

[warm elm]

thats it?

thats shit

ok so

there is apparently a formula for shortest line which

admittedly i forgot but i found it

here it is

[haughty prism]

I didn't know that even exists

[warm elm]

well

now you do

[haughty prism]

Haha

[warm elm]

so just to break it down a bit the

a2 - a1 is just

difference in position vectors

and b1 x b2 is just cross product of the direction vectors

[haughty prism]

Ok 👍

[warm elm]

and then you just sorta throw it together apparently and it works?