Vector problem solution check?

[misty raptor]

I did this question like this, but i feel like i messed something up. Thoughts?

[timber kraken]

Part a is correct

Part b is incorrect

You need to solve (3i-2j)-(-i-4j)

Check calculation of Part e too, it should be -3+8=5

[misty raptor]

oh darn, thank you for pointing it out

[misty raptor]

part 3?

[timber kraken]

Part c is also correct, you can fix part d after fixing part b

Part f is correct

[timber kraken]

I meant e, sry typo

[misty raptor]

Also, dumb question, but I am puzzled about the vector subtraction

why would it be different than the addition?

seems like a crucial point i need to keep track of

oh I see now

[timber kraken]

It's not different

[misty raptor]

I took the negative of solely the y components

that was my mistake

[timber kraken]

Addition should be : (3i-2j)+(-i-4j)

[misty raptor]

yeah that makes sense

I got 4i + 2j for my new value

[timber kraken]

That's correct

[misty raptor]

updated version

thank you a lot though, I still struggle with vectors despite years of relearning them haha

also, this practise problem made me think of a question

what exactly is the value you get of the vector product formula i did in this problem?

i guess you can derive the components out of it

[timber kraken]

It's the magnitude of the resultant vector of A×B

[misty raptor]

would it be considered the full answer then if it is only the magnitude?

i honestly did all of the orange text part because I didn't want to do the vector product components formula haha

[timber kraken]

You mean the one with the determinant?

[misty raptor]

yes

too long

the answer sheet was pretty small for that too

[timber kraken]

Practice makes it shorter. I would suggest to do it anyway so you get more familiar with it and find it easier to use

[misty raptor]

I always aim to try to conceptualise concepts such as those, vectors have always been that sore thumb that I couldn't really truly ' understand'

I know how to compute the dot product, but I struggle to understand what it is, or what is it trying to represent

[timber kraken]

The actual formula is |A||B|sin(theta)[n(cap)], where n(cap) denotes the direction of the resultant vector

[misty raptor]

same for the vector product if that makes sense

[timber kraken]

The resultant vector is always perpendicular to A and B

[misty raptor]

oh is the sign of the resultant indicative of that?

perpendicular in the positive z direction

interesting

Hm

I wanna try out the right hand rule for this

[timber kraken]

Personally, for me, seeing them as an operation made it easier to digest. Also, if you see what they represent geometrically, you develop a deeper understanding of dot and cross product

[misty raptor]

lets see

[timber kraken]

Not really, n(cap) is just a unit vector perpendicular to A and B.

https://math.stackexchange.com/questions/77/understanding-dot-and-cross-product

[timber kraken]

This thread can help you understand what usefulness dot and cross product serve as operations

https://math.stackexchange.com/questions/805954/what-does-the-dot-product-of-two-vectors-represent

https://math.stackexchange.com/questions/2634517/whats-an-intuitive-explanation-behind-cross-products-being-vectors-when-dot-pr

Check out these two threads too

[misty raptor]

I did try to study them for a bit

from what i understand

the scalar product is the "parallel" unit of say, vector A, on vector B while we disregard the perpendicular force of vector A

but that just makes it harder for me to understand in a way, why would there not be a direction of that unit by the end of it?

[misty raptor]

thank you! i will make sure to check them after my Physics class in a bit

[timber kraken]

Think of it this way instead : when we are dealing with vectors, sometimes we need to find the magnitude of this "parallel" unit, so we have designed an operation called the "dot product" in order to find it

We don't need this magnitude to have a direction, as it doesn't serve us any purpose, that is why the dot product isn't designed to have a direction

[misty raptor]

Hm I understand the idea

I think i need some real-world association to remove the abstractness

How could the "dot product" be used in real life if as such?

[timber kraken]

It's used all the time in physics

To calculate work done for example

One of the above threads do explain this

[old bobcat]

part e is incorrect?

[misty raptor]

Why is that?

I did get 5

In the second picture

[misty raptor]

Yeah i know of that. Was more wondering of a more specific application

[old bobcat]

o_o okie

[timber kraken]

Vectors are used in computer science too

[misty raptor]

😅

[misty raptor]

Oh really? That's interesting

[old bobcat]

Did you also correct part f finally?

[old bobcat]

from the updated version?

[misty raptor]

Yes

I guess this is solved now. Thank you!

.close

[fierce tide]

Solved

Post marked as solved by @trim spoke.

Use .unsolved if this was a mistake.

[old bobcat]

Ah I just wanted to check. It should be 10 not 10.13, right?

[misty raptor]

Oh what, seems like i mixed up what you meant

Why would it be 10?

[old bobcat]

of course because sine of your angle would be 10/(√17 √13), no?

[misty raptor]

Ahh I see what u mean now

[misty raptor]

When I calculated the angle I did put the approximately equal to sign because it wasn't exact

Which led up to this

Should've put on the sign for that too

This is a physics homework I suppose, and they are alright with approximations I believe

[old bobcat]

btw just so you know, you didn't have to do the cos/sine thing... you could've just went:

A x B = (3)(-4)k - (-2)(-1) k = -10 k

which means 10.13 is definitely not your answer even if you say you approximated

because the cross product is supposed to be a vector

[misty raptor]

I see... I guess I have another misconception

[misty raptor]

Btw shouldn't it be - 14?

[old bobcat]

🤦 yes

[misty raptor]

Sigh i could've just used that since the i and j would be 0

Oh well, learning experience even if it's too late

Huh so the right answer would've given me that 14

But why was it wrong then

Did i do the trigonometric angles wrongly

I will redo those Ig let's see

[old bobcat]

ah because you wrote down A dot B = -11 from your previous solution

and didn't correct it to 5

[misty raptor]

aaaaaa

man

istg vectors will be the end of me

[old bobcat]

the same as me :D

[misty raptor]

It's wild, I have been introduced to them 3-4 years ago? But I still never seem to click with them

Things like trigonometry, algebra, calculus, discrete math I have been able to relatively greatly get better at

But them vectors