Question

Let V = 2i + 2k and W = 2i + j + k
Find the angle between v and w.

I know that acos((V•W)/|V||W|) = theta and that asin(|VxW|/|v||w|) = theta as well. But when I do the dot product method I get the wrong answer and when I do the cross product method I get the right answer, any suggestions as to why this might be?

Answer 1

for v.w, what u get ?

Answer 2

I get 6

Answer 3

look u are right. so which part u stucked ?

Answer 4

I got acos(3/(2√2))

Answer 5

how com, show to me please, for checking where is ur mistake

Answer 6

can u determine the magnitude of vectors v and w ?

Answer 7

magnitude of v is 2√2 and magnitude of w is 6... oohh so it should be acos(1/2√2) but that still isn't the right answer?

Answer 8

yeah, u have right for magnitude of vector v, for magnitude of w it should be √6 right ?

Answer 9

sqrt (2^2 +1^2 + 1^2) = sqrt(4+1+1) = sqrt(6)

Answer 10

that's for |w|

Answer 11

oooooohhhh right right I forgot about the √ I guess it was just a simple mistake haha

Answer 12

haha, nope :)
so, what's the measure is it ?

Answer 13

arccos(1/2 sqrt(3)), right ?

Answer 14

it is very familiar in trigonometry, the value of cosine which have value
1/2 sqrt(3)

Answer 15

I got arccos(3/2√3)

Answer 16

which is pi/6 which is what I get with the cross product.

Answer 17

though one :)
ys, 30 degrees or pi/6 its answer

Answer 18

Thank you for your help!

Answer 19

you're welcome :)