RosettaCodeData/Task/Vector-products/00-TASK.txt

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:
        <big> A = (a<sub>1</sub>,  a<sub>2</sub>,  a<sub>3</sub>) </big>
        <big> B = (b<sub>1</sub>,  b<sub>2</sub>,  b<sub>3</sub>) </big>
        <big> C = (c<sub>1</sub>,  c<sub>2</sub>,  c<sub>3</sub>) </big>
then the following common vector products are defined:
* '''The dot product''' &nbsp; &nbsp; &nbsp; (a scalar quantity)
:::: <big> A • B = a<sub>1</sub>b<sub>1</sub> &nbsp; + &nbsp; a<sub>2</sub>b<sub>2</sub> &nbsp; + &nbsp;  a<sub>3</sub>b<sub>3</sub> </big> 
* '''The cross product''' &nbsp; &nbsp; &nbsp; (a vector quantity)
:::: <big> A x B = (a<sub>2</sub>b<sub>3</sub>&nbsp;  - &nbsp; a<sub>3</sub>b<sub>2</sub>, &nbsp; &nbsp; a<sub>3</sub>b<sub>1</sub> &nbsp; - &nbsp; a<sub>1</sub>b<sub>3</sub>, &nbsp; &nbsp; a<sub>1</sub>b<sub>2</sub> &nbsp; - &nbsp; a<sub>2</sub>b<sub>1</sub>) </big> 
* '''The scalar triple product''' &nbsp; &nbsp; &nbsp; (a scalar quantity)
:::: <big> A • (B x C) </big>
* '''The vector triple product''' &nbsp; &nbsp; &nbsp; (a vector quantity)
:::: <big> A x (B x C) </big>


;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: <code>a • b</code>
# Compute and display: <code>a x b</code>
# Compute and display: <code>a • (b x c)</code>, the scalar triple product.
# Compute and display: <code>a x (b x c)</code>, the vector triple product.


;References:
* &nbsp; A starting page on Wolfram MathWorld is &nbsp; {{Wolfram|Vector|Multiplication}}.
* &nbsp; Wikipedia &nbsp; [[wp:Dot product|dot product]]. 
* &nbsp; Wikipedia &nbsp; [[wp:Cross product|cross product]]. 
* &nbsp; Wikipedia &nbsp; [[wp:Triple product|triple product]].


;Related tasks:
* &nbsp; [[Dot product]]
* &nbsp; [[Quaternion type]]
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