This problem involves taking the dot product of two vectors A & B. The vectors are defined as: A = 4i+3j+6k B = 2i-j-4k The dot product calculation will be performed using IDL. Put simply, vector multiplication, dot product, is done by multiplying like indices directly and then summing the result. The calculations follow: IDL> A = [4,3,6] IDL> B = [2,-1,-4] IDL> C = total(A*B) IDL> print, C -19.0000