The function of crossprod in R puzzled me.
I would like to calculate the cross product of two vectors. According to my text book, it defines like this:
a = (ax, ay, az)
b = (bx, by, bz)
then, the cross product of a and b is:
a X b = (ay*bz-az*by, az*bx-ax*bz, ax*by-ay*bz)
It can also write in a determinant format.


But the crossprod or tcrossprod function in R appeared not calculate the cross product. Suppose I enter this:
> a = c(1, 2, 3)
> b = c(2, 3, 4)
> ab = crossprod(a, b)
> ab
     [,1]
[1,]   20
> ab = tcrossprod(a, b)
> ab
     [,1] [,2] [,3]
[1,]    2    3    4
[2,]    4    6    8
[3,]    6    9   12


Does any know how to calculate cross product in R. Or I have to write the function myself?
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