A vector is defined as having three dimensions as being represented by an ordered collection of three numbers:   (X, Y, Z).

If you imagine a graph with the   x   and   y   axis being at right angles to each other and having a third,   z   axis coming out of the page, then a triplet of numbers,   (X, Y, Z)   would represent a point in the region,   and a vector from the origin to the point.

Given the vectors:

        A = (a1,  a2,  a3) 
        B = (b1,  b2,  b3) 
        C = (c1,  c2,  c3) 

then the following common vector products are defined:

 The dot product       (a scalar quantity)
  A • B = a1b1   +   a2b2   +   a3b3  
 The cross product       (a vector quantity)
  A x B = (a2b3  -   a3b2,     a3b1   -   a1b3,     a1b2   -   a2b1)  
 The scalar triple product       (a scalar quantity)
  A • (B x C) 
 The vector triple product       (a vector quantity)
  A x (B x C) 


Task

Given the three vectors:

        a = ( 3,    4,    5)
        b = ( 4,    3,    5)
        c = (-5,  -12,  -13)

 Create a named function/subroutine/method to compute the dot product of two vectors.
 Create a function to compute the cross product of two vectors.
 Optionally create a function to compute the scalar triple product of three vectors.
 Optionally create a function to compute the vector triple product of three vectors.
 Compute and display: a • b
 Compute and display: a x b
 Compute and display: a • (b x c), the scalar triple product.
 Compute and display: a x (b x c), the vector triple product.


References

   A starting page on Wolfram MathWorld is   Vector Multiplication .
   Wikipedia   dot product. 
   Wikipedia   cross product. 
   Wikipedia   triple product.


Related tasks

   Dot product
   Quaternion type


#include<stdio.h>
 
typedef struct{
	float i,j,k;
	}Vector;
 
Vector a = {3, 4, 5},b = {4, 3, 5},c = {-5, -12, -13};
 
float dotProduct(Vector a, Vector b)
{
	return a.i*b.i+a.j*b.j+a.k*b.k;
}
 
Vector crossProduct(Vector a,Vector b)
{
	Vector c = {a.j*b.k - a.k*b.j, a.k*b.i - a.i*b.k, a.i*b.j - a.j*b.i};
 
	return c;
}
 
float scalarTripleProduct(Vector a,Vector b,Vector c)
{
	return dotProduct(a,crossProduct(b,c));
}
 
Vector vectorTripleProduct(Vector a,Vector b,Vector c)
{
	return crossProduct(a,crossProduct(b,c));
}
 
void printVector(Vector a)
{
	printf("( %f, %f, %f)",a.i,a.j,a.k);
}
 
int main()
{
	printf("\n a = "); printVector(a);
	printf("\n b = "); printVector(b);
	printf("\n c = "); printVector(c);
	printf("\n a . b = %f",dotProduct(a,b));
	printf("\n a x b = "); printVector(crossProduct(a,b));
	printf("\n a . (b x c) = %f",scalarTripleProduct(a,b,c));
	printf("\n a x (b x c) = "); printVector(vectorTripleProduct(a,b,c));
 
	return 0;
}