Question

Help with vectors?
Let u be a vector with initial point (3,8) and terminal point (1,1).
Let v be a vector with initial point (3,-4) and terminal point (0,0).
Find the component form of the vectors and calculate the value of 3u - 2v.

Answer 1

@Kainui @iambatman

Answer 2

u (3,8) , (1,1)
v (3,-4) , (0,0)

Answer 3

So we need to find component form first -- any ideas on how you think we might start for that?

Answer 4

No :/

Answer 5

it's pretty much 2nd coordinate - 1st coordinate
I'll demonstrate for u ...

Answer 6

u = < 1 - 3 , 1-8 >

u = < -2 , -7 >

Answer 7

That's the component form of u ^
Can you find the component form of v? it would be done the same way

Answer 8

< 0 -3, 0 + 4 >?

Answer 9

Right! what does that simplify to be?

Answer 10

< -3, 4 >

Answer 11

Mhm!

Answer 12

So the first part of that problem is done. The next part is to find 3u - 2v, right?

Answer 13

Yes

Answer 14

Luckily that's gonna be pretty easy too,
we just take our component forms and plug them in

Answer 15

3(< -2, -7 >) - 2(< -3, 4>)?

Answer 16

good! then what do we do with the 3 and the 2?

Answer 17

Do I have to multiply 3*-2, 3*-7, -2*-3 and -2*4?

Answer 18

Yes! If you want to leave the negative outside you can
so just multiply 3 through and then multiply 2 through

I want to leave the negative outside because we're going to subtract the vectors

Answer 19

oh ok

Answer 20

= < -6 , -7 > - < -6 , 8 >

So, what's our final answer?

Answer 21

< -12, 1 >

Answer 22

no, < 0, -15 >

Answer 23

Yep

Answer 24

Thanks :)

Answer 25

The answer in my lessons says < 0, -29 > @Miracrown

Answer 26

alrighty. let me double check the work on my paper

Answer 27

Do you want me to show you their steps?

Answer 28

so what don't you get?

Answer 29

No, don't show me their steps. I know what happened

Answer 30

what is 3 times -7?

Answer 31

Ok, I get this one @nincompoop , but looking at the other, I don't get them

Answer 32

-21

Answer 33

Right. we forgot to distribute the 3 to the -7
so we should have had:
<-6,-21> - <-6,8>

Answer 34

oh, ok :)

Answer 35

now subtract those two vectors, and you'll get the answer that matches theirs :)
Sorry about that :'(

Answer 36

it's fine :) it was only a practice problem

Answer 37

thank god

Answer 38

you're welcome :)

Answer 39

do you still need help or what?

Answer 40

I think we're dun

Answer 41

then you must be done

Answer 42

dun dun dun

Answer 43

Yep, all done, at least for now :)