How to calculate the mixed product of vectors? Given a parallelepiped with three ABC vectors as edges, how to calculate its volume? If we know that V parallelepiped = ABC three vector products, we can't calculate determinant

Volume v = a point product (b cross product C)
Let a = (A1, A2, A3) B = (B1, B2, B3) C = (C1, C2, C3)
V=|A B C|=A1B2C2+A2B3C1+A3B1C2-C1B2A3-A2B1C3-A1B3C2
The multiplication and addition of the number in the direction of "\" minus the multiplication and subtraction of the number in the direction of "/" in the 3 × 3 determinant

The calculation of vector product
Let a, B and C be nonzero vectors, then (AXB) XC = [D]
A.ax(bxc) B.(bxa)xc C.cx(axb) D.cx(bxa)

There is no definition of vector outer product, only vector scalar product (inner product), vector product, mixed product and so on
(a,b,c)·(x,y,z)=ax+by+cz
(a,b,c)×(x,y,z)=(bz-cy,cx-az,ay-bx)
(a,b,c)×(x,y,z)·(m,n,p)=m(bz-cy)+n(cx-az)+p(ay-bx)

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How to calculate the mixed product of vectors? Given a parallelepiped with three ABC vectors as edges, how to calculate its volume? If we know that V parallelepiped = ABC three vector products, we can't calculate determinant