vector arithmetic

//+ addition ;

v1 = {a,2,c}+{1,b,3};

show v1;

save as addition;

//- addition ;

v1 = {a,b,c} - {0, 0, 0};

show v1;

save as subtraction;

// v - v = 0 ;

v1 = {a,b,c} ; v2 = v1 - v1;

show v1 also v2;

save as subtraction;

// v1 + v2 = v2 + v1 ;

v1 = {a,b,c} ; v2 = {1,2,3};

v3 = v1+v2; v4 = v2+v1;

v5 = v3 == v4;

show v1 also v2 also v3 also v4 also v5;

save as subtraction;

// (v1 + v2) + v3 = v1 + (v2 + v3);

v1 = {a,b,c} ; v2 = {1,2,3}; v3 = {p,q,r};

//fist add v1 and v2 then v3; tmp1 = v1+v2;

v5 = tmp1 +v3;

//first add v2 and v3 then v1; tmp2 = v2 +v3;

v4 = v1 + tmp2;

v6 = v4 == v5;

show v1 also v2 also v3 also v4 also v5 also v6;

save as addition;

SCALE

v = u * {a, b, c, d, e, f};

show v;

save as scale;

v = u * {a, b, c, d, e, f};

show v;

save as scale;

v1 = {x, y}; v2 = v1 + v1; v3 = 2 * v1;

show v2 also v3;

save as scale;

v1 = {x, y}; v2 = v1 + v1 + v1; v3 = 3 * v1;

show v2 also v3;

save as scale;

v = t *{a, b, c, d, e, f} * s;

show v;

save as scale;

v = (s+t) * {a, b, c, d, e, f};

show v;

show expand[v];

show simplify[v];

save as scale;

v = 0 * {a, b, c, d, e, f};

show v;

save as scale;

v = 1 * {a, b, c, d, e, f};

show v;

save as scale;

NEGAGIVE

v1 = {1,2}; v2 = -1*v1; //v2 = -v1;

//list of pivots; pivots = {{0,0}, {0,0}}; //list of vectors; vectors = {v1,v2};

vectorplot pivots vectors;

save as scale;