Question

vector calculus: u=3i+2j-4k and v=i+6j+5k, find scalars a and b so that the vector w=5i-18j-32k can be written in the form w=au+bv

Answer 1

set up system of equations

3a +b = 5
2a +6b = -18
-4a +5b = -32


a = 3
b= -4

Answer 2

Where did you get those equations from?

Answer 3

<5,-18,-32>=a<3,2,-4>+b<1,6,5>

Answer 4

3a+b=5

Answer 5

however i'm not sure if there is infinite solutions in this case but dumbcow has set it up right

Answer 6

from what outkast is doing

Answer 7

And what would that be?

Answer 8

you could use linear matrix to solve

Answer 9

basically i'm taking the vector components and equaling them

Answer 10

Why are you allowed to do that?

Answer 11

so if you have a<3,2,1> or <v1,v2,v3> , then the scalar of that would be <3a,2a,1a>

Answer 12

No, first of all, where does a and b even come into play?

Answer 13

yes cv = <kv1,kv2,kv3>

Answer 14

We were given u and v with i,j, and k components

Answer 15

i mean kv = and he's asking in the question what scalars a and b are

Answer 16

What is kv? kilovolts?

Answer 17

lol k is scalar

Answer 18

None of this is making any sense

Answer 19

if k is a scalar then
kv=<kv1,kv2,kv3>

Answer 20

I don't know what that means

Answer 21

it means that if you times a vectors by a scalar your components will be times the scalar

Answer 22

<i,j,k>=<v1,v2,v3>

Answer 23

Vector Calc 101....In order for me to understand, you'd have to do a complete presentation of it

Answer 24

But that's okay. I'm going to leave and come back in five minutes. When I come back, I might understand it better than you.

Answer 25

yeah i'm taking the class right now, and it can be confusing at times.... so many equations

Answer 26

anyways dumbcows answer is correct, does not have infinite solutions however i wouldn't know how to explain it without using what i've learned in MAT2880

Answer 27

it tally makes sense, its just multiplying each vectors by its corresponding one. By the way dumcows, wasnet there a shortcut by cross multiplication? or am i confusing that for are of parallelogram

Answer 28

shortcut? i dont know maybe, i am not aware of one

you could also set up a matrix and solve using reduced row echelon form

Answer 29

Thank you dumbcow....thats what i did also but i got stuck when i realized i have 3 eqns nd 2 unknowns

Answer 30

Understanding this from a geometrical standpoint is very helpful