Finding the Cross Product and Angle Between Two Vectors

[yb1013]

Homework Statement

Two vectors are given by Avec = -1 i + 2 j and Bvec = 4 i + 2 j

Find A X B

Find the angle between A and B

The Attempt at a Solution

Okay well I got the First part of the problem, I know that A X B is -10, but when I do everything for the angle I keep getting the wrong answer.

After I finish with my calculating I come up with cos (theta) = -10/10 which would simplify to 180 degrees, but that's wrong...

Can someone please help me out, I don't understand where I am going wrong

Thank You!

 

[nasu]

If you want the cosine of the angle you need the dot product (not the cross product).
The angle is 90 deg, the two vectors are perpendicular.

If you use the cross product, you'll get sin (theta)=1 and theta = 90 deg.

 

[yb1013]

oo ok, thank you

 

[whybother]

It's important to remember how the cross-product is defined before you look at this problem. The cross-product is an operation in a 3-D vector space that produces a third vector.

In this case:
(-1, 2, 0) $$\times$$ (4, 2, 0) = (0, 0, -10)

The cross product also gives you:
$$a \times b = \sin{\theta} \nhat$$

You might have an easier time looking at the dot product only.

But if your 2D vectors aren't actually lying in a 3D space, do not use the cross product at all, as it is not well defined.