What is the magnitude of the vector product?

1. Jun 21, 2007

Equilibrium

1. The problem statement, all variables and given/known data
Find the vector product $$\vec{A} \times \vec{B}$$ (expressed in unit vectors ) of the two vectors given. What is the magnitude of the vector product?
$$\vec{A} = 5.00\hat{i} + 2.00\hat{j}$$
$$\vec{B} = 3.00\hat{i} - 1.00\hat{j}$$

2. Relevant equations
$$\vec{A}\vec{B}\sin(\theta)$$

3. The attempt at a solution

using pythagorean theorem i found that the resultant of the two is
5.39 and 3.16

plus the total angle w/c is 40.2

using the formula mentioned above i found the answer as 11k and magnitude of 11.0

what i am confused is that it has a different answer from the back of my book w/c is -$$-17\hat{k},17.0$$
who is wrong the book or me???
and pls show me why?

Last edited: Jun 21, 2007
2. Jun 21, 2007

Staff: Mentor

Your answer seems correct to me. As a double check, find the cross product by multiplying the components.

3. Jun 21, 2007

Equilibrium

the unit vectors should be
using the determinant rule
z =AxBy - AyBy
z = 5(-1)-2(3)

z = -11

-11\hat{k}

and the magnitude is where u use ABsin(theta) =11.0

4. Jun 21, 2007

Staff: Mentor

Why do you say your answer is wrong? (Note that both methods gave you the same answer.)

5. Jun 21, 2007

Equilibrium

how?

...
the components shud be positive??
now im confused

Last edited: Jun 21, 2007
6. Jun 21, 2007

Staff: Mentor

I'm not sure what you are asking. In your first post, you showed how you arrived at your solution. (Yes, your sign was wrong, but all you needed was the magnitude.) I said it was correct and asked you to double-check using a different method. You did and got the same answer for the magnitude. So why do you think your answer is wrong?

7. Jun 21, 2007

Equilibrium

i thought this has two questions
Finding vector product AXB expressed in unit vectors and magnitude

8. Jun 21, 2007

D H

Staff Emeritus
Are you sure that you have both vectors stated properly? For example, flipping the x and y components of B yields the answer in the book: $$\vec B = 1.00\hat i - 3.00\hat j$$. This is an easy mistake to make -- either by you or by the authors.

9. Jun 21, 2007

Staff: Mentor

Good eye, D H. I'll bet that's it.

10. Jun 21, 2007

Equilibrium

so the book is wrong then...

11. Jun 21, 2007

Staff: Mentor

One of you must be. For the problem as you described it here, your solution is correct. (Make sure you copied it correctly, as D H suggested.)