#Conceptual question about unit vectors

74 messages · Page 1 of 1 (latest)

lucid terraceBOT
high sable
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Conceptual question about unit vectors

keen fulcrum
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Hmm.....

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Vectors.....

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They get around nowadays

high sable
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The slide says unit vectors have a magnitude of 1. Is this for every single vector? Like what if I have a vector that has components of 2i, 3j, and 2k?

keen fulcrum
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What's the question?

high sable
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Or would the magnitude still be 1

keen fulcrum
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"unit vector" means the scalar = 1 ....

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it's used to conceptually explain stuff related to vectors

bleak trellis
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😭

high sable
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The magnitude of the overall vector isn’t 1 but the magnitude scalar wise of the unit vector is always 1?

keen fulcrum
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Vectors are scalars x Direction.... the direction is i, j, k for x, y, z space

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Yes, unit vectors always have scalare of 1 because you're only concerned with looking at the i,j,k direction

high sable
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Oh ok

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Also

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I dont have a qst abt how to solve this problem

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But like

keen fulcrum
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So you can speak and understand vectors in terms of direction only... then when you grasp it, apply a magnitude to it (scalar) which allows it to be represented into x,y,z space

high sable
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When it says a = 16 b = 12 c =20 what does that mean conceptually? Does that mean the vector a magnitude is 16 and vector b mag is 12 and vector c mag is 20?

bleak trellis
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no

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wait you can find the angles

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and just solve it via cross product

torn kindle
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u want to know why unit vectors or basis vectors exists ?

keen fulcrum
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So treat those lengths as hints to plot it in x,y ... then you can sum up the results

high sable
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Yeah ik how to solve it i was just confused if the unit vectors in those problems would still have a magnitude of 1

keen fulcrum
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so for instance, they say a = 16 ... so that's i=16, j = 0, k = 0 (k is for Z in 3D which isn't apart of this chart)

torn kindle
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or by unit vectors

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i meant basi vector

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for that case, the basis vectors r unit vectors and orthonormal

keen fulcrum
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For (a) it asks about magnitude... which is the scalar...

high sable
high sable
keen fulcrum
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for (b) is asks about direction of a x b... which is (ib-ia), (jb -jb)

high sable
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Yup

torn kindle
high sable
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Ik how to solve the problem i’m just confused on whether or not the unit vectors of that problem still have a magnitude of 1 bc it’s like

Vector a 16i 0j 0k
Vector b 0i 12j 0k

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So that would mean the unit vectors magnitude are still 1?

torn kindle
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i j k r unit vectors

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u can think of these vectors as sticks

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which makes up other vectors

high sable
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Ah ok i think i got it

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So

torn kindle
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like 3 horizontle sticks and 2 verticle sticks makes up vector (3,2)

high sable
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Unit vectors is basically just the i,j,k and they always have a magnitude of 1

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But the vector itself can have a magnitude greater than 1

torn kindle
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if the basis r orthonromal ( maginitude = 1 and r perpenducular to each other) then use pythagoras theorem to find the magnitude of the vector formed by those sticks

torn kindle
high sable
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Ohhh

keen fulcrum
high sable
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Ok i think i have a better idea now

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Also

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What level of math is this?

torn kindle
high sable
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Oh

torn kindle
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well vectors comes in linear algebra tho

high sable
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Ig i forgot learning it

torn kindle
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also part of pre calc

high sable
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I kinda remember doing matrices in precalc a bit

keen fulcrum
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So say you have a car in your garage that needs an equation to drive, but you give it 1 instead of 0 so it doesn't catch on fire from mathematical spontaneous combustion until you need to drive it lol

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Then when you're ready to drive, you hop in and plug in 15 and it drives 15 miles in a direction for you

torn kindle
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yes

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but in a particular direction

keen fulcrum
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Then when you're done and park back in the garage, you don't plug in zero because it'll blow up, so you plug 1 back in

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lame example I know but i had to chuckle

high sable
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It helped tho lol

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Thank u guys

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.solved

lucid terraceBOT
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Solved

Post marked as solved by @high sable.

Use .unsolved if this was a mistake.

torn kindle
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np