Question

if U = 3i-4j, and V = 2i+3j then the angle Ө between U and V are ?

Answer 1

Have you guys learned dot or cross products in your class?

Answer 2

yes!

Answer 3

you can pick either one. i prefer dot products though

Answer 4

so it's U dot V = ac + bd ?

Answer 5

U dot V = 3(2) + -4(3) ?

Answer 6

correct. U dot V = ac + bd = |u||v|cos(theta)

Answer 7

are those 2 formulas the same ?

Answer 8

yes, they are equivalent. you can just write it as
ac+bd = |u||v|cos(theta)

Answer 9

solve for theta and you got your angle :)

Answer 10

I'm sorry i got -6 for U dot V then what do i do from there ?

Answer 11

|u| is the magnitude of the u vector. so 3^2 + 4 ^ 2 = c ^2, solve for c and get 5.
|v| is the magnitude of the v vector. so 2^2 + 3^2 = c^2 solve for c and get sqrt(13)

Answer 12

-6 = 5* sqrt(13) * cos(theta)

Answer 13

ohh i see

Answer 14

so the answer is : cos(theta) = 11xsqrt(13) that's it ?

Answer 15

\[\cos(\theta)=-6/(-5*\sqrt(13))\]
\[\theta = \cos^{-1} (-6/(5*\sqrt(13))\]

Answer 16

i don't have a calculator on me :( but that should give you your answer

Answer 17

how did u move that -6 o_0 and the cos theta

Answer 18

don't you add the -6 to the right side ? and minus cos(theta) to the left side ?

Answer 19

ahh nvm i got it, you used all 3 formulas at the sametime, and just plugging it in =.=

Answer 20

Thanks @alexandercpark