How do I find the geometric definition of (i+J)cross(i-j)?

[HappMatt]

heres the problem.

im supposed to use geometric definition to find. (i+J)cross(i-j)

I know: v x w=IIvIIIIwIISin[theta] and that The answer comes out to be -2k

But what i don't get is looking at the solution manual they show [theta]=pi/4 which i have know clue where that comes from.

I was thinking that i could use (v)dot(w) =Cos[theta] to get[theta] but that ends up being pi/2 not pi/4 like the solution manual says.

I think the solution maunual is wrong after futher review [Theta} should equal pi/2, not Pi/4

 

[FrogPad]

I take it you did not preview your post. Or maybe I'm drunk and don't know it... but what are you saying?

 

[HappMatt]

well i think i may have wasted an hour due to 2 things,
1: the soution manual is wrong [theta]=pi/2
2:the dot product equals 2 and for somereason i was taking the inverse sign instead of the inverse cosine wheni entered it so that was confusing me. I think i can chaulk this mistake up to dyslexia possibly though.

if I am still wrong please correct me(ps but not on my spelling/grammar that has always sucked only slightly improves every yr).

 

[FrogPad]

Oh wait...

IIvII = $|\vec v |$

 

[FrogPad]

I guess I'm confused with this:

$$(i+J) \times (i - j)$$

is $i$ supposed to be $\hat i$, or a complex number, or what?

You also have $J$ and $j$ so that is confusing...

you're grammar seems to be fine, it the way you express the mathematical statements that I'm unsure...

 

[HappMatt]

Oh wait...

IIvII = $|\vec v |$

i totally need this latex thing to simplify life

Oh wait...

IIvII = $|\vec v |$

no but i think this may be right
$||\vec v ||$

 

[HappMatt]

sorry about the confusion i should probally go and figure out that whole latex way of writting stuff out as to make it easier to read.

 

[HappMatt]

So here is the question re stated what is the angle between the 2 vectors v and w where:
v=(i+j)
w=(i-j)

 

[FrogPad]

How do you find the angle between two vectors in two dimensional space?

 

[HappMatt]

How do you find the angle between two vectors in two dimensional space?

yeah i guess that's another way of saying it, but i think i figued it out.

 

[FrogPad]

what did you get?In regards to this question:
So here is the question re stated what is the angle between the 2 vectors v and w where:
v=(i+j)
w=(i-j)I got pi/2... but shoot, it's been awhile. Maybe I'm doing this wrong.

 

[HappMatt]

what did you get?


In regards to this question:
So here is the question re stated what is the angle between the 2 vectors v and w where:
v=(i+j)
w=(i-j)


I got pi/2... but shoot, it's been awhile. Maybe I'm doing this wrong.

i think your right its the darn solution manual and the people at Wiley publishing that have no clue what they are doing.

 

[FrogPad]

I hate crap like that. It makes you second guess what you are doing, even when you are doing it right.

 

[Hurkyl]

If you're typing equations in ASCII, you should use the pipe symbol (|) to denote absolute values, norms, and stuff:

||v x w|| = ||v|| ||w|| |sin theta|