Vector Arithmetic
+ and - operators
What: Addition and Subtraction of Vectors
Why: Detailed computations
Time To Complete: 2 hours
+
//+ addition ;
v1 = {a,2,c}+{1,b,3};
show v1;
save as addition;Output:
"v1" → {1 + a, 2 + b, 3 + c}'//' : Comment Operator instructing the Grammarian to ignore its sentence
'v1' : identifier for a variable or variable name
'=': Assignment Operator copying the Right Hand Side to Left Hand Side
'{ }' : curly brackets, enclosing the list of elements in between
'a,2,c' : Elements of the vector enclosed in '{ }' brackets
';' : Delimiter called semicolon indicating the end of a Free Form sentence, separating sentences
'show': textually displays the followed variables
'save as': instructs the Grammarian to save the Free Form script and all its interim computations in cloud objects
-
//- subtraction ;
v1 = {a,2,c}-{1,b,3};
show v1;
save as subtraction;Output:
"v1" → {-1 + a, 2 - b, -3 + c}Properties
0-vector
//+ 0 ;
v1 = {a,b,c} + {0, 0, 0};
show v1;
save as subtraction;Output:
"v1" → {a, b, c}//- 0 ;
v1 = {a,b,c} - {0, 0, 0};
show v1;
save as subtraction;Output:
"v1" → {a, b, c}© 2012-Present CCN Studios
Creative Commons Attribution-NonCommercial-ShareAlike 4.0
*: Scale Factor
What: Scale a vector
Why: Computations to alter the length and direction of a vector
Time To Complete: 1-3 hours
Multiply a vector by a numeral from the left.
v = 5.4 * {x,y};
show v;
save as scale;Multiply a vector by a numeral from the right.
v = {x,y}*5.4;
show v;
save as scale;Output
"v" → {5.4*x, 5.4*y}u ought to be a variable/symbol or a numeral. u cannot be another vector.
v = u * {a, b, c, d, e, f};
show v;
save as scale;Output
"v" → {a*u, b*u, c*u, d*u, e*u, f*u}Scale Factor < 0
What: Negative scale factor
Why: How to reverse a vector to point in the opposite direction
Time To Complete: 1-3 hours
v1 = {1,1};
v2 = -1*v1;
//list of pivots;
pivots = {{0,0}, {0,0}};
//list of vectors;
vectors = {v1,v2};
vectorplot pivots vectors;
save as scale;Output
