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## Main Question or Discussion Point

Hello, I have a question about why I can't determine the angle between two vectors using their cross product.

Say there are two vectors in the XY-plane that we want to find the angle between:

The method to do this would be to work out the

In the example above, this gives a correct angle of 165°.

However, I feel like it should be possible to arrive at the same answer using a

However, using this method results in an angle of 15.3°.

I must be missing something in the way all of this works and wondered if anyone could provide me with the knowledge I'm missing!

Thanks!

Andy

Say there are two vectors in the XY-plane that we want to find the angle between:

**A**= -2.00**i**+ 6.00**j**

B= 2.00B

**i**- 3.00**j**

The method to do this would be to work out the

*scalar*product of the vectors, calculate the magnitude of each vector, and use these to determine the angle via this relationship:**A**⋅**B**= AB cos ∅In the example above, this gives a correct angle of 165°.

However, I feel like it should be possible to arrive at the same answer using a

*vector*product method instead. So I tried calculating the vector product, and used it with the calculated magnitudes of the vectors and the following relationship:**A**X**B**= AB sin ΦHowever, using this method results in an angle of 15.3°.

I must be missing something in the way all of this works and wondered if anyone could provide me with the knowledge I'm missing!

Thanks!

Andy