As part of a retirement project, I have decided to brush up my maths (I have degrees in geology and in maths, but from a long time ago!) and tried some basic vector operations, including the Mathematica Cross product function, but ran into a puzzle. If you take the cross product of the two vectors:

A = 2i-3j-k

B= i+4j-2k

And work it out by hand, you get AXB= 10i+3j+11k, which is the same as in the book that I took this example from.

The Mathematica function Cross[{2I,-3I,-I},{I,4I,-2I}], which I would expect to get the same answer, gives {-10,-3,-11}, that is the negative of the hand worked and the text book answer.

I had the same result when I tried examples from other text books.

I expect that there is a farirly simple explanation, but I am very new to Mathematica, and haven't figured out what it is, and would appreciate some advice.