Question

Find a ⋅ b.
a = <2, 4>, b = <2, 5>

Answer 1

these are the answer choices
<4, 9>

24

<4, 20>

16

Answer 2

and your choice is?

Answer 3

well I thought it was <4,20> but that clearly isn't an answer choice

Answer 4

hmm, a dotproduct produces a number, not a vector

Answer 5

stack, multiply, add the resutls

Answer 6

a = <2, 4>
b = <2, 5>
4 + 20

Answer 7

so would it be 24?

Answer 8

i organize them like this to avoid misplacing the information

all i have to do then is multiply down the columns and add the resutls

Answer 9

yes, 24

Answer 10

ah ok I see how you do this...

Answer 11

:) practice makes perfect ... and then dementia sets in lol

Answer 12

haha :) would you mind helping me with a few more?

Answer 13

one more, need to start heading to bed

Answer 14

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

u = <2, -4>, v = <3, -8>

Answer 15

this involves the definition of a dotproduct

\[|u||v|cos(a)=u\cdot v\]

Answer 16

so we can start with dotting u to v, what do we get?

Answer 17

what is a?

Answer 18

a is alpha, or angle .... its what we will end up solving for

also notice that when we dot a vector to itself:

(x , y)
(x , y)
----------
x^2 + y^2

the results are almost the length .... sqrt(x^2 + y^2) defines the length of a vector

Answer 19

I don't really understand...

Answer 20

do the dotproducts:

u.v
u.u
v.v

we will use these in the "formula" in order to solve for the required angle

Answer 21

what am I multiplying? Idk at all

Answer 22

the first think you posted asked you to find the dot product of 2 vectors, i demonstarted what to do .... you said you "ah ok I see how you do this..."

now given:

u = <2, -4> and v = <3, -8>

find u dot v
and u dot u
and v dot v

Answer 23

ao you basically do them separately and then add them together at the end?

Answer 24

do them seperately, and then we will use them as needed. at the moment we simply need to know what they are.

Answer 25

ok so u.v is 38
uu is 20
and vv is 73?

Answer 26

let me chk :)

u = <2, -4>
v = <3, -8>
6 + 42 = 40


u = <2, -4> and v = <3, -8>
u = <2, -4> and v = <3, -8>
4+16 = 20 9 + 64 = 73

correct

Answer 27

how do I solve for the angle then?

Answer 28

now we can work the problem\[|u||v|cos(a)=u\cdot v\]
\[|a|=\sqrt{a\cdot a}\] sooo
\[\sqrt{20}~\sqrt{73}~cos(a)=40\]
divide off the sqrts and inverse the cosine to detemrine a
\[cos(a)=\frac{40}{\sqrt{20}~\sqrt{73}}\]
\[a=cos^{-1}\left(\frac{40}{\sqrt{20}~\sqrt{73}}\right)\]

Answer 29

ok well I tried plugging it into my calculator but it keeps saying error

Answer 30

thats cause the result is bigger than 1 ....

Answer 31

what would that mean?

Answer 32

3.0°

6.0°

-7.0°

16.0°
these are the answer choices

Answer 33

u = <2, -4>
v = <3, -8>
6 + 32 = 38 you had the right number, i messed it up ... said it was 40

Answer 34

\[a=cos^{-1}\left(\frac{38}{\sqrt{20}~\sqrt{73}}\right)\]
much better

Answer 35

http://www.wolframalpha.com/input/?i=arccos%2838%2Fsqrt%2820*73%29%29

Answer 36

so 6 degrees?

Answer 37

yep

Answer 38

all that work defining the dots, and i used 40 instead of 38 :) i mentioned the dementia part right?

Answer 39

thank you so much for your help:) and yes I remember you mentioning dementia:p lol well have a good night you should probably go to bed:)

Answer 40

thnx, and good luck ;)