Question

MEDALS AWARDED!!!

Evaluate the expression:

v ⋅ w

Given the vectors:

r = <5, -5, -2>; v = <2, -8, -8>; w = <-2, 6, -5>

Answer 1

is it asking for the dot product?

Answer 2

yes , dot product of vectors

Answer 3

ok so just multiply the corresponding components and add them together

Answer 4

so it would be 2x-2/-8x6,-8x-5?

Answer 5

(2*-2)+(-8*6)+(-8*-5)=?

Answer 6

-4+(-42)+40?

Answer 7

=-4?

Answer 8

@wilfley ??

Answer 9

6*8=48 so it would be -4+(-48)+40=-12

Answer 10

alright, bad multiplication from my part...but is that all?

Answer 11

that's it, the dot product of vectors is just a number

Answer 12

i do not use r?

Answer 13

and one more question...

Answer 14

Find a ⋅ b.

a = <2, 4>, b = <2, 5>

= 24???
@wilfley ?

Answer 15

yes

Answer 16

thank you... and one more please lol

Answer 17

Find the angle between the given vectors to the nearest tenth of a degree.

u = <6, -1>, v = <7, -4>

@wilfley

Answer 18

just a sec

Answer 19

cos(theta)= (dot product of u and v)/(magnitude of u times magnitude of v)

Answer 20

dot product is 46? how do i find the magnitude?

Answer 21

@wilfley

Answer 22

\[\left| u \right|=\sqrt{(6)^2+(-1)^2}\]

Answer 23

is it 6.08? @wilfley

Answer 24

46/6.08=7.5?

Answer 25

you also need the magnitude of v and then multiply that number to the \[\sqrt{37}\] I would give it like that instead of as a decimal unless the question asks for the approximate answer

Answer 26

then you will have a number that you can use

Answer 27

\[\frac{ 46 }{ \sqrt{37}\sqrt{65} }=\cos (\theta)\]

Answer 28

\[\sqrt{47} x \sqrt{65}????\]

Answer 29

i got .97

Answer 30

yeah, then take the inverse cosine of that whole mess and you will have your answer

Answer 31

my answer choices are
20.3°

10.2°

0.2°

30.3°

Answer 32

i got 14 degrees @wilfley

Answer 33

cool, I get 20.3

Answer 34

let me show you the work, it will just take a minute

Answer 35

alright, yea i see what i did wrong... thanks a ton @wilfley

Answer 36

\[\frac{ 46 }{ \sqrt{37}\sqrt{65} }=\frac{ 46 }{ \sqrt{2405} } so.....\cos^{-1} (\frac{ 46 }{ \sqrt{2405} })=(\theta)\]

Answer 37

yeaa i see it now... thank you for you help @wilfley !!!!!

Answer 38

sure!