Step by Step solution about How to resolve the algorithm Vector products step by step in the Ruby programming language

The provided Ruby code defines a Vector class and demonstrates how to perform various vector operations, including the scalar triple product and vector triple product. A brief explanation below:

1. require 'matrix': This line imports the Matrix library, which provides support for working with matrices and vectors in Ruby.

2. class Vector: This defines a custom Vector class, which represents a 3D vector with three components (x, y, z).

3. def scalar_triple_product(b, c): This method calculates the scalar triple product of the current vector (self) with vectors b and c. The scalar triple product is defined as the dot product of self with the cross product of b and c.

4. def vector_triple_product(b, c): This method calculates the vector triple product of the current vector (self) with vectors b and c. The vector triple product is defined as the cross product of self with the cross product of b and c.

5. a = Vector[3, 4, 5]: This line creates a Vector object a with the components (3, 4, 5).

6. b = Vector[4, 3, 5]: This line creates another Vector object b with the components (4, 3, 5).

7. c = Vector[-5, -12, -13]: This line creates a third Vector object c with the components (-5, -12, -13).

8. puts "a dot b = #{a.inner_product b}": This line calculates the dot product of vectors a and b and prints the result. The dot product is a scalar value that measures the similarity between two vectors.

9. puts "a cross b = #{a.cross_product b}": This line calculates the cross product of vectors a and b and prints the result. The cross product is a vector that is perpendicular to both a and b.

10. puts "a dot (b cross c) = #{a.scalar_triple_product b, c}": This line calculates the scalar triple product of vectors a, b, and c, and prints the result.

11. puts "a cross (b cross c) = #{a.vector_triple_product b, c}": This line calculates the vector triple product of vectors a, b, and c, and prints the result.

In summary, this code showcases the use of the Vector class to perform various vector operations, including the scalar triple product and vector triple product. It demonstrates how to create vector objects, calculate dot products and cross products, and perform more complex vector operations.

require 'matrix'

class Vector
  def scalar_triple_product(b, c)
    self.inner_product(b.cross_product c)
  end

  def vector_triple_product(b, c)
    self.cross_product(b.cross_product c)
  end
end

a = Vector[3, 4, 5]
b = Vector[4, 3, 5]
c = Vector[-5, -12, -13]

puts "a dot b = #{a.inner_product b}"
puts "a cross b = #{a.cross_product b}"
puts "a dot (b cross c) = #{a.scalar_triple_product b, c}"
puts "a cross (b cross c) = #{a.vector_triple_product b, c}"