dVector
dVector is an OISC invented by User:None1 and inspired by Vector, it uses a 3-dimensional vector.
Data
As said above, Vector uses a 3D vector called A, it is initially (0,0,0).
A vector literal is represented by 3 real numbers separated by spaces.
Command
V2 V3 c D
B and D are 3D vectors, c is a real number. The command means: If det[A,V2,V3] equals to c, then (add A by D and jump to the start of program).
There is an output command, it is not required so it does not count in the number of commands:
V2 V3 c D W2 W3
(Print the value of det[A,W2,W3] then add A by D and jump to the start of program) if det[A,V2,V3] equals to c. Whether as number or as character depends on implementation.
ndVector
Of course, we can use other dimensions instead of 3 dimensions, that gives us nVector (n is the dimension number).
Command(s) are the same as vector except that a vector literal uses n numbers instead of three, and other n-1 vectors are needed to calculate determinant. For example, the commands in 4dVector will be like this:
V2 V3 V4 c D
and:
V2 V3 V4 c D W2 W3 W4
Computational class
When there are at least 3 dimensions, dVector (ndVector) is Turing complete because it's equivalent to Vector.
The determinant calculated will be like: c1*a1+c2*a2+c3*a3+... where ci are constants and ai are dimensions of A, which is exactly what dot product does.