Question

Find the angle between the given vectors to the nearest tenth of a degree. (2 points)

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

3.0°
6.0°
-7.0°
16.0°

Answer 1

i got -7.0 not sure lol if i got it correct

Answer 2

how do you test if it is correct?

Answer 3

not sure how! actually

Answer 4

what approach did you take?

Answer 5

if using vectors, id use the dot product identity

Answer 6

the last thing i got was (19sqrt365)/ 365 but the decimal form doesnt match my answer

Answer 7

you want to take a cosine inverse if you did the rest right

Answer 8

|u| |v| cos(a) = u.v

cos(a) = u.v/(|u| |v|)

a = inverseCos(u.v/(|u| |v|)) which will either give radians or degrees depending on your calculator setting

Answer 9

a·b = ax·bx + ay·by = 2 · 3 + (-4) · (-8) = 6 + 32 = 38

Answer 10

You can find the angle between two vectors (also used to find the angle between two lines in an intersecting point) with the equation:
\[Cos \alpha =\frac{ x_u x_ v + y_u y_v }{ \sqrt{x_u ^2 + y_u ^2 }\sqrt{x_v ^2 + y_v ^2} }\]
of if you prefer:
\[Cos \alpha = \frac{ U.V }{ \left| \left| U \right| \right|\left| \left| V \right| \right| }\]

Answer 11

idk why its so far apart but i used the dot approach

Answer 12

well, define your lengths and your dot product lets start there and correct if needed

Answer 13

okay so im confused on the set up then

Answer 14

@Owlcoffee /cdot makes a nice latex dot \(u\cdot v\)

Answer 15

I'll have that in mind, thanks Amistre.

Answer 16

u = <2, -4>
sqrt(4+16)


v = <3, -8>
sqrt(9+64)

u = <2, -4>
v = <3, -8>
6+32

these are our parts right?

Answer 17

yes

Answer 18

then

a = cos^(-1)(38/(sqrt(20*73)))

Answer 19

if your calcultor is in radian mode, then it doesn give degrees

Answer 20

ohh okay let me calculate this

Answer 21

a=cos^-1 (19/sqrt365)?

Answer 22

no need to simplify anything, the calculator is capable of working with the stated values

Answer 23

if your inputting them is awkward, then calculate

20*73 = k

take the sqrt of it, write it down if need be or stick it in the calcs memory

38 / k = m

now take the inverse cos of m

what type of calcuator you using?

Answer 24

online calculator!

Answer 25

online, then just do this

http://www.wolframalpha.com/input/?i=cos%5E%28-1%29%2838%2F%28sqrt%2820*73%29%29%29

Answer 26

idk if im inputting the correct thing

Answer 27

ohh so it would be 6.009!

Answer 28

yes, or in this case 6.0 seems rnded

Answer 29

oh i see!! I was forgetting about the radians conversion

Answer 30

thank you :)!!!!!!!

Answer 31

your welcome

Answer 32

would you mind helping me with another! @amistre64