Inner product of the two vectors u = (ux, uy) and v = (vx, vy) is defined as:

u*v = (ux, uy) * (vx, vy) = ux * vx + uy * vy

A. Write a C program to compute the inner product of two vectors using the definition. Function should take as arguments the four vector components and return their inner product. Function prototype should be:

double inner_product (double ux, double uy, double vx, double vy);

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It can be shown that the cosine angle formed between two vectors u and v is given by the expression:

cos() = u*v / sqrt((u*u) * (v*v))

B. Write C program that will compute the angle for any two given vectors u and v

(i) input the two vectors by readin the 2 cartesian compnent values for each one of the vectors (4 numbers in total)

(ii) use the function in part A to compute the inner dot products involved in the expression above (notice there are 3 inner products in that expression)

(iii) compute the angle using the acos() funct from math.h

(iv) print out the value for angle in degrees (notice the acos() funct reutrns values in radians- multiply result of acos() funct by 180/pi)

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C. Use previsouly developed codes as functions and develop new code that will be computing all three angles of a plane triangle and will report any angles that are obtuse by identifying the vertex the obtuse angle responds to

(i) input the coordinates of the 3 triangle vertices as 3 pairs of x and y coordinates

(ii) for each of the triangle's vertices form, you need to form the vectors that correspond to the triangle's sides for example for vertex 1, the two vectors should be:

u = (x2-x2, y2-y1) and v = (x3-x1, y3-x1)

then repeat for other two vertices

(iii) find the angle formed by the two vectors using the codes developed in part A and try to shorten the new code by converting the code of part B into a function: make a function out of the entire part B code; the prototype for this function could look like:

double angle (double ux, double uy, double vx, double vy);

(iv) test the angles for obtuseness and report the results