Question

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

u = <8, 7>, v = <9, 7>

-8.3°

1.7°

3.3°

13.3°

Answer 1

do you know how to do a dot product ?

Answer 2

yes

Answer 3

8*9 + 7*7
72 + 49
119

Answer 4

check your addition

meanwhile, the other definition of dot product is
\[ a \cdot b = |a| |b| cos\theta \]
where |a| means length of a
and | b | is length of b

Answer 5

i mean 121, sorry wrong math

Answer 6

so you now know
\[ a \cdot b = 121 \]
and
\[ 121= |a| |b| \cos\theta \]
you need to find |a| and |b|

Answer 7

ok so sqrt(145) for a and sqrt(98) for b

Answer 8

are you doing u = <8, 7>, v = <9, 7>
?

Answer 9

|u|^2 is u dot u

Answer 10

ok how do you find the length of a and of b, im not quite sure what i did but it must be wrong

Answer 11

find |u|^2 = u dot u
then take the square root
do the same for v

Answer 12

ok give me just a second to do that then

Answer 13

let's use u and v and not a and b, to avoid confusion

Answer 14

u^2 = 113
v^2 = 130

Answer 15

yes, so |u| = sqrt(113)
and |v|= sqrt(130)

Answer 16

\[ 121= \sqrt{113} \sqrt{130} \cos\theta \]
solve for theta

Answer 17

.9983308057 = cosθ

Answer 18

now take the inverse cosine of both sides

Answer 19

they want the angle to the nearest 10th of a degree

Answer 20

.0577868302

Answer 21

I think you are in "radian mode" put your calculator in degree mode

Answer 22

or multiply .0577868302 * 180/pi and round to the nearest tenth

Answer 23

its about 3.3 degrees correct?

Answer 24

yes

Answer 25

ok thankyou

Answer 26

and one more thing

Evaluate the expression:

v ⋅ w

Given the vectors:

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

Answer 27

for this one do i just multiply all the v and w vectors. then add?

Answer 28

you multiply corresponding components and sum

Answer 29

-12

Answer 30

is that write phi