What is the angle between vectors A and B?

[MozAngeles]

Homework Statement

Two vectors A and B have magnitude A = 2.99 and B = 3.10. Their vector product is A X B = -4.98 k + 2.08 i . What is the angle between A and B?

Homework Equations

C= ABsinθ
C=A X B

The Attempt at a Solution

θ= arcsin C/(⎮A⎮⎮B⎮)
so i found the magnitude for C, then divided by (a times b), then took the sin inverse. Where i got theta = 53 degrees but this was wrong. Can someone please point me in the right direciton?

 

[vela]

Suppose you have the three vectors A=i, B=i+j, and C=-i+j. Then |A|=1 and |B|=|C|=sqrt(2). You also have AxB = k and AxC = k, so sin(A,B) = sin(A,C) = 1/sqrt(2).

Sketch the vectors in the xy-plane and you'll see what's going on. The same thing is happening in your problem.

 

[MozAngeles]

Hi, I'm sorry i sketched it out and it still does not make sense... I'm really still quite lost...

 

[vela]

What's the angle between A and B and between A and C? (from the sketch)

 

[ehild]

The Attempt at a Solution

θ= arcsin C/(⎮A⎮⎮B⎮)
so i found the magnitude for C, then divided by (a times b), then took the sin inverse. Where i got theta = 53 degrees but this was wrong.

You miscalculated something. Are you sure you did not use inverse cosine instead of sine? Show your work in detail.

ehild

 

[vela]

Oops, I guess I should have solved the problem myself.

Never mind what I said above. Listen to ehild.

 

[ehild]

Vela,

Is it possible and how to find out from these data if the angle enclosed by the vectors A and B is less than or greater than 90°? I do not see it now.

ehild

 

[HallsofIvy]

You can't, just from the lengths. The length of [math]A\times B[/math] is the same as the length of [math]A\times (-B)[/math]. If the angle between A and B is less than 90 degrees then the angle between A and -B is larger than 90 degrees.

 

[vela]

No, you can't, not without more info.

 

[ehild]

Thanks.

ehild

 

[MozAngeles]

I was doing it right initially, my calculations were wrong. Thanks for your help anyways!