- 2)
- (6 pt) A common operation that needs to be performed on
vectors is the
*dot product*or*scalar product*. This is defined as

where*x*and*y*are two vectors of length*n*.

Write a function that will compute the dot product of two vectors and a main program to test your function. Use the vectors in the datafile`hw31_1.in`

to test your function.

Note that there is already an intrinsic F90 function that does this. Don't use the intrinsic function for this assignment. - 2)
- (10 pts)
Subroutines and functions can (and often do) call other subroutines
and functions. Whenever you
need to write a new function, it's a good idea to make use of
any existing functions you have already written. Consider the
binomial coefficient
*C*(*n*,*k*) defined by:

This quantity is comprised of three factorial operations. If you have a function available to compute*n*!, you can use this routine to compute*n*!,*k*! and (*n*-*k*)!. You can then combine these calculations to produce*C*(*n*,*k*).Write a function that will compute the binomial coefficient given the values of

*n*and*k*. Your function should compute the factorials in the binomial coefficient formula by calling the factorial function we wrote in the previous class. The template for your function should beFUNCTION getbinomial(n,k)

Use your function to compute the values of*C*(3,1),*C*(5,3),*C*(14,5), and*C*(10,0).