Find the angle between the vectors u and v.

Question

anonymous · Answer

u=cos(pi/6)i +sin(pi/6)j and v=cos(3pi/4)i + sin(3pi/4)j

phi · Answer

u dot v = |u| |v| cos(theta)

turingtest · Answer

Is there something about this formula that is giving you a problem in this one?
I know we've done these before.

anonymous · Answer

when i did this formula i got something really weird and idk what i did wrong. how would you do it?

turingtest · Answer

what did you get for |u| and |v| ?

anonymous · Answer

1

anonymous · Answer

because cos(pi/4) is sqrt3/2. and sin (pi/4) is 1/2

anonymous · Answer

so u= (sqrt3/2, 1/2)

anonymous · Answer

and v=(-sqrt2/2, sqrt2/2)

anonymous · Answer

right?

turingtest · Answer

it's one for both, but the easier way to see it is that both magnitudes are of the form$$\sqrt{\sin^2\theta+\cos^2\theta}$$and we know that that is always one.

btw
cos(pi/4)=sqrt2/2
but I think you meant cos(pi/6) above ?

anonymous · Answer

oh yea i did sorry!

turingtest · Answer

let me try it...

turingtest · Answer

about 1.832 radians is what I got

turingtest · Answer

which is 105 degrees

anonymous · Answer

hmm okay. thats an option

turingtest · Answer

what did you get for the dot-product?
are you not getting the same answer?

turingtest · Answer

$$u=\frac{\sqrt3}{2}i+\frac{1}{2}j$$$$v=-\frac{\sqrt2}{2}i+\frac{\sqrt{2}}{2}j$$so what is their dot-product ?

anonymous · Answer

sqrt6/4 + sqrt2/2

turingtest · Answer

you lost a negative sign:
-sqrt6/4 + sqrt2/2

turingtest · Answer

now you should get the right answer...

turingtest · Answer

oh sorry, also forgot a four
-sqrt6/4 + sqrt2/4

anonymous · Answer

oh i got it now! thanks :)