need help , Vector problems

[pearl pine]

Need help for No.6 and 7.

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[pearl pine]

Shall I connect AC?

I don't know where to start

[sour night]

Hmm...

Well, this would be pretty easy if we used coordinates.
Just geometrically, though... Not sure.

[pearl pine]

I will wait for someone who can help...exam tomorrow

[sour night]

Well, in any case, you can always try the coordinate approach.

Let's try (7) now.

I've tried it, it seems a bit easier.

[pearl pine]

K

Wait pls

[sour night]

Yeah, that one seems easier. I could solve it, at least 😅

[pearl pine]

This seems to be the case

I should have drawn AB at the bottom lol

[sour night]

Well, I've drawn it like this.

Doesn't particularly matter.

[pearl pine]

Wait

I think I can do this

[sour night]

Also, I proved it by calculating BF and BE, instead.

[pearl pine]

Lemme try

If I get this , 6 is the only problem then

[sour night]

Sure!

I'll try thinking on (6) a bit more.

[pearl pine]

Thanks

EB = 2b - a

EF = -1/3b - a

AF = -1/3b

I think the latter 2 could be wrong

Ah right

Forget the (-) from all b and the answer should be right

Right? @sour night

[sour night]

EF isn't correct.

Can you show how you found it?

[pearl pine]

Sorry for handwriting

Ahhh

2/3a

Forgot about 1/3(2a-b)

[sour night]

So, what is EF?

[pearl pine]

1/3(b+a)?

[sour night]

No, that's not correct.

[pearl pine]

My bad CF:FD = 2:1

It's the opposite of what I am using

Trying again

2/3b - 1/3 a?

[sour night]

Yeah, nice!

So, if EB = -a + 2b and EF = -(1/3)a + (2/3)b, what can we say?

[pearl pine]

So AF should be 2/3 (b+a)

[sour night]

We don't need AF.

[pearl pine]

Uhh.... what can we say? ;-;

[sour night]

Well, do you notice anything in particular about their coordinates?

[pearl pine]

I don't use coordinates yet , we only learn about addition and some stuff of vectors for now

[sour night]

Well, we can notice that all coordinates of EF are 1/3 of the coordinates of EB.
So, EF = (1/3)EB.

So, EF and EB are collinear. Then, what can we say about the points E, F, B?

[pearl pine]

F lies on EB?

[sour night]

Well, yes. But most importantly, it means that E, F and B lie on the same line.

Which is what we needed.

[pearl pine]

But doesn't Collinear means the same thing?

[pearl pine]

Can't we just find EB with EA + AB = EA + 2AD = -a + 2b ?

[sour night]

I was talking about vectors before, not points.
What I meant is that if two vectors with the same initial point are collinear, then their initial point and endpoints are also collinear.

[pearl pine]

Oh

But why do we need them to be on the same line though?

[sour night]

Well, we are asked to prove that...

[pearl pine]

Ouch

I should have read the question to the end

Sorry

😅

[sour night]

No worries!

Still, I wonder how to solve (6).
As I said, if we use coordinates of vectors, that would be very easy. But not sure how to do it without that.

[pearl pine]

Doing the next ones as we talk , I got 3 more Vector exercises+ Some Differentiation

[sour night]

Oh, ok.

If they are significantly different, it might be better to make a new help thread.

[pearl pine]

Okay, looks like I ain't getting a good sleep tonight

[sour night]

Hm. If it isn't very late, maybe it's better to rest for half an hour, then continue?

[pearl pine]

It's 8 pm here so I could rest a little

Lemme finish one more exercise

Only 8 problems

[sour night]

Sure! We can also discuss it if you need it.

[pearl pine]

Thanks

So if there is no vector sign above a side , I can use AB= BA right?

[sour night]

Well, if you don't write an arrow above it, then yes.
If you do, then AB = -BA.

In any case, |AB| = |BA|.

[pearl pine]

Finished it

I can rest 15 mins

[sour night]

Nice!

[pearl pine]

I am worried about my mental health...

[sour night]

What's wrong?

[pearl pine]

Nothing particular, just worried about Social science and Physics too

Math is my 3rd most worried subject

[fallen locust]

im not exactly sure, but if it is a regular arent all the sides the same length

[pearl pine]

Yeah

[fallen locust]

then it would just be 1/2d + 1/2b

i think at least

obviously if you invert the direction its negatives

[pearl pine]

Where does d comes from?

[fallen locust]

question said in terms of b and d

AB is d

so u need to include both b and d

[pearl pine]

... it's a and b

;-;

[pearl pine]

Also can you pls explain this? I am not really good at vectors

[fallen locust]

kk

[fallen locust]

mb read it wrong

[fallen locust]

basically u know that AB = BC

as it is a regular octagon so all same sides

[sour night]

Well, the lengths are obviously the same. But we are dealing with vectors.

The directions are different.

[fallen locust]

yh , but i was trying to explain it

cuz op asked

[pearl pine]

Hmm

We can't say a=b just because AB=BC either

Idk what to do with the knowledge of all sides are equal

[fallen locust]

it is, question tells you all sides are equal

so the distance is the same for everything

but cuz its a vector directions matter

[pearl pine]

How do we get pass directions ?

[fallen locust]

the arrows

it says AB

so u draw an arrow from A to B

and label that as a

[pearl pine]

I know it , I was just asking how do we solve this using directions + (AB=BC)

[fallen locust]

BC*

[pearl pine]

😅

[fallen locust]

if AB=BC

a=b

as it is the same vector for both

just with aa different value assigned

[pearl pine]

So?

[fallen locust]

im going to give a/b imaginary values

i think thats the best way to explain for now

so until u underatand, pretend a = 1

if a=1

and a=b

b=1

but the question wants you to make use of both a and b

and a+b=2

but you know what ur answer shoud be, which is half of that

because u are only looking for 1 side length of each

2/1

or 1/2(a+b)

or 1/2a + 1/2b

@pearl pine

[pearl pine]

The question is to find the other sides in term of a and b

[pearl pine]

Which side is this for?

[fallen locust]

all of them

[fallen locust]

@pearl pine have you solved it yet ?

[pearl pine]

Nope , but I did well in my exam

I will close the case I guess

Thanks

+close