Question

Let u = <-7, -2>. Find 4u.

Answer 1

simply multiply each component of by 4

Answer 2

i got <28, -8> im not sure if that is right

Answer 3

hmm what happened to the \(-\) sign of first component ?

Answer 4

oh! so it will be -28, -8?

Answer 5

<-28, -8> is \(\large \color{red}{\checkmark}\)

Answer 6

thank! can you help me with a few other questions i got wrong on my homework?

Answer 7

I'll try, ask...

Answer 8

Given that P = (5, 9) and Q = (13, 12), find the component form and magnitude of ->over PQ

Answer 9

i had problems with this and just randomly answered <-8, -3>, 73

Answer 10

\(\large \overrightarrow{PQ} = \overrightarrow{OQ} - \overrightarrow{OP} = \langle 13, 12\rangle - \langle 5, 9\rangle = ?\)

Answer 11

i am confused?

Answer 12

to subtract two vectors, we just subtract each components :

\(\large \overrightarrow{PQ} = \overrightarrow{OQ} - \overrightarrow{OP} = \langle 13, 12\rangle - \langle 5, 9\rangle = \langle 13-5, ~12-9 \rangle = ? \)

Answer 13

All we're doing is subtraction only :)

13 - 5 = ?
12 - 9 = ?

Answer 14

8 and 3?

Answer 15

but i am looking at the answer choices and they include 73 or sqrt 73

Answer 16

Yes !
\(\large \overrightarrow{PQ} = \langle 8, ~3 \rangle \)

Answer 17

thats the component form of PQ ^

Answer 18

You need to find its magnitude still

Answer 19

magnitude = \(\large \sqrt{8^2 + 3^2} = ?\)

Answer 20

14?

Answer 21

how ?

Answer 22

magnitude = \(\large \sqrt{8^2 + 3^2} = \sqrt{64 + 9} = \sqrt{73}\)

Answer 23

so <8, 3>, \[\sqrt{73}\]

Answer 24

what about Let u = <-5, 1>, v = <7, -4>. Find 9u - 6v, I answered <-36, -18>

Answer 25

this one i am very confused by

Answer 26

multiply u by 9
multiply v by 6

subtract

Answer 27

u = <-5, 1>

9u = ?

Answer 28

<-5, 1> i subtract that?

Answer 29

multiply it by 9

Answer 30

u = <-5, 1>

9u = 9*<-5,1> = <-45, 9>

Answer 31

see if u can find `6v`

Answer 32

<63, -36>?

Answer 33

Nope.

v = <7, -4>

6v = 6*<7, -4> = ?

Answer 34

<42, -24>?

Answer 35

Yes !
now subtract

Answer 36

9u - 6v = <-45, 9> - <42, -24>
= ?

Answer 37

so -54, 66?

Answer 38

this is where i get confused a little because i subtract the neg 45 from 9? or do i subtract the neg 54 and 66?

Answer 39

you need to subtract the corresponding components

Answer 40

9u - 6v = <\(\color{red}{-45}\), \(\color{green}{9}\)> - <\(\color{red}{42}\), \(\color{green}{-24}\)>

Answer 41

<-87, 33> ???

Answer 42

9u - 6v = <\(\color{red}{-45}\), \(\color{green}{9}\)> - <\(\color{red}{42}\), \(\color{green}{-24}\)>
= <\(\color{red}{-45-42}\), \(\color{green}{9--24}\)>
= <\(\color{red}{-87}\), \(\color{green}{33}\)>

Answer 43

Yes ! looks you nailed it !!

Answer 44

thank you! im going to try Let u = <9, 4>, v = <-2, 5>. Find u + v. can you tell me if i get the answer right?

Answer 45

okay i got <7,9>? @ganeshie8

Answer 46

Excellent !!

Answer 47

you've become the maestro of vectors !!

Answer 48

yay, thank you very much!

Answer 49

np, you're welcome :)