the lengths of the diagonals of parallelograms whose sides are vectors

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Erros

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Hello everyone, please help me with this task, I can't do it and I would like to understand and do it.

Calculate the lengths of the diagonals of a parallelogram whose sides are a vectors:

[imath]a\vec{} = 2m\vec{} + n\vec{}[/imath]
[imath]b\vec{} = m\vec{} - 2n\vec{}[/imath]
if [imath]|m\vec{}\;|= \sqrt{3}[/imath] , and [imath]|n\vec{}\;|=2[/imath] , and [imath]\angle{\vec{m},\vec{n}} = \pi/6[/imath]
 
Erros said:
Hello everyone, please help me with this task, I can't do it and I would like to understand and do it.

Calculate the lengths of the diagonals of a parallelogram whose sides are a vectors:

[imath]a\vec{} = 2m\vec{} + n\vec{}[/imath]
[imath]b\vec{} = m\vec{} - 2n\vec{}[/imath]
if [imath]|m\vec{}\;|= \sqrt{3}[/imath] , and [imath]|n\vec{}\;|=2[/imath] , and [imath]\angle{\vec{m},\vec{n}} = \pi/6[/imath]
Click to expand...
Do you know

the laws of parallelogram for vector addition?​
 
Erros said:
Hello everyone, please help me with this task, I can't do it and I would like to understand and do it.

Calculate the lengths of the diagonals of a parallelogram whose sides are a vectors:

[imath]a\vec{} = 2m\vec{} + n\vec{}[/imath]
[imath]b\vec{} = m\vec{} - 2n\vec{}[/imath]
if [imath]|m\vec{}\;|= \sqrt{3}[/imath] , and [imath]|n\vec{}\;|=2[/imath] , and [imath]\angle{\vec{m},\vec{n}} = \pi/6[/imath]
Click to expand...
Consider the parallelogram ABCD.

If the vector sum of  \(\displaystyle \overrightarrow{a}\) & \(\displaystyle \overrightarrow{b}\) may be represented by the parallelogram's diagonal AC then what vector sum will get you a vector that may be represented by the other diagonal?
Paralellogram.jpg
​
If you aren't already familiar with the "law of parallelogram vector addition" then Google it but don't use the Cuemath site (there's a confusing error in their explanation).

Hint: Use Exact Value(s) for any trigonometric ratios involved.​
 
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Erros said:
I think I could calculate over this View attachment 32623, but I'm not sure, that's why I don't know how to do it
Click to expand...
Did you research the "law of parallelogram vector addition" (as I suggested) and draw up a diagram (similar to mine) as @Steven G suggested?
We really shouldn't be helping you any further until we have seen 'evidence' that you have followed those suggestions and produced some written attempt(s) for us to look at (then we can confirm your work is correct or offer advice on how to adjust/improve it).
However, I'm going offline shortly so, to save time, look at the summary I have inserted for you (below). That should enable you to complete your task with no further difficulties.
The "law of parallelogram vector addition" is basically just the Cosine Rule (which is the main 'formula' used to calculate any parallelogram's diagonals; even a square's).
You are, therefore, really only interested in the magnitude of the vectors involved and the angles between them. So now get sketching & calculating and show us your results, please.
Paralellogram-Diagonals.jpg
​
PS: @Subhotosh Khan. Can you explain why I am getting "intermediary" posts appearing after I have posted something, please? There was no sign of this OP's 'reply' to your post #2 (Re-quoted in Bosnian?) in what is (now) numbered as Post #4 (submitted by the OP). That post (#4) definitely was not there (I checked before posting) when I submitted my post (now #5!). This happened to me in another thread too, recently, where I posted something and when I looked back at the thread later someone else's post had suddenly 'appeared' above mine! ???
 
The Highlander said:
Did you research the "law of parallelogram vector addition" (as I suggested) and draw up a diagram (similar to mine) as @Steven G suggested?
We really shouldn't be helping you any further until we have seen 'evidence' that you have followed those suggestions and produced some written attempt(s) for us to look at (then we can confirm your work is correct or offer advice on how to adjust/improve it).
However, I'm going offline shortly so, to save time, look at the summary I have inserted for you (below). That should enable you to complete your task with no further difficulties.
The "law of parallelogram vector addition" is basically just the Cosine Rule (which is the main 'formula' used to calculate any parallelogram's diagonals; even a square's).
You are, therefore, really only interested in the magnitude of the vectors involved and the angles between them. So now get sketching & calculating and show us your results, please.
Paralellogram-Diagonals.jpg
​
PS: @Subhotosh Khan. Can you explain why I am getting "intermediary" posts appearing after I have posted something, please? There was no sign of this OP's 'reply' to your post #2 (Re-quoted in Bosnian?) in what is (now) numbered as Post #4 (submitted by the OP). That post (#4) definitely was not there (I checked before posting) when I submitted my post (now #5!). This happened to me in another thread too, recently, where I posted something and when I looked back at the thread later someone else's post had suddenly 'appeared' above mine! ???
Click to expand...
That happens to me too - and those problems I have declared to be above my pay-grade.
 
The Highlander said:
PS: @Subhotosh Khan. Can you explain why I am getting "intermediary" posts appearing after I have posted something, please? There was no sign of this OP's 'reply' to your post #2 (Re-quoted in Bosnian?) in what is (now) numbered as Post #4 (submitted by the OP). That post (#4) definitely was not there (I checked before posting) when I submitted my post (now #5!). This happened to me in another thread too, recently, where I posted something and when I looked back at the thread later someone else's post had suddenly 'appeared' above mine!
Click to expand...
I'm sure you're aware that new users need 5 approved posts by a moderator (cough cough... @Subhotosh Khan) before it is made available to the public. Look at how many posts the OP made. The OP made the post before you, it just didn't get approved.
What is your excuse now SK ?
 
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I calculated diagonal 1, and diagonal 2 on the same principle as the first one, I hope this is a good way and is this okay, did I make a mistake and is this what is actually required in the task?
20220507_211254.jpg
 
Steven G said:
Come on SK, you are correct using the approximately equal sign but then you ruined everything by then putting an equal sign.
Click to expand...
It is CORRECT in Engineering Sciences to use "equal to" sign when the level of accuracy has been stated (through statement of significant digit or other means.
 
Subhotosh Khan said:
It is CORRECT in Engineering Sciences to use "equal to" sign when the level of accuracy has been stated (through statement of significant digit or other means.
Click to expand...
Fine, then please use an equal sign on an Engineering Sciences forum.
 
Subhotosh Khan said:
It is CORRECT in Engineering Sciences to use "equal to" sign when the level of accuracy has been stated (through statement of significant digit or other means.
Click to expand...
Steven G said:
Fine, then please use an equal sign on an Engineering Sciences forum.
Click to expand...
An aside, to stop you two fighting! ?
While idly browsing Maths 'stuff', I came across a worksheet (q.v.) on the nzmaths website. Quickly scanning through it, my eye was caught by the figure in their answer to Q3, Part iii and the text below it, right at the end of the worksheet. (I have included a pic, below, showing relevant excerpts from the worksheet but you can see the whole original using the link above.)

It seems (to me) that there is something wrong with either the question or the answer!

2022-05-08-1.png
​

I reckon the answer should read:-

From the diagram we can quickly see that B = 130º and C = 20º. Then by the Sine Rule,
b = 223.98*. Then the height of the mountain (hill?) is 223.98 sin 30º = 111.99m.     
*to 5 s.f. ?                                                           ​

Either that or the question should be:-

A mountain has an elevation of 29º and 30º from two points that form             
a horizontal line with the base of the mountain. The two points are               
100m apart. What is the height of the mountain?                             ​

Am I missing something? (As is often the case.)
Or should I point out their mistake to them?
 
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