Vector functions in scripts

Vectors can be defined in scripts by putting the components in square brackets: A = [1,2,3];. The following vector functions have been defined.

length(A) - length of vector $|\vec{A}|=\sqrt{A_x^2 + A_y^2 + A_z^2}$
dot(A,B) - scalar product of two vectors $\vec{A}\cdot\vec{B} = A_xB_x + A_yB_y + A_zB_z$
dot(a,B) - scalar times a vector $ a\vec{B} = aB_x\,\hat{x} + aB_y\,\hat{y} + aB_z\,\hat{z}$
cross(A,B) - cross product $\vec{A}\times\vec{B}$
unit(A) - unit vector $\vec{A}/|\vec{A}|$
vadd(A,B) - vector addition $\vec{A}+\vec{B}=(A_x + B_x)\,\hat{x} + (A_y + B_y)\,\hat{y} + (A_z + B_z)\,\hat{z}$
vsub(A,B) - vector subtraction $\vec{A}-\vec{B}=(A_x - B_x)\,\hat{x} + (A_y - B_y)\,\hat{y} + (A_z - B_z)\,\hat{z}$

The function dot(A,B) is overloaded. If the arguments A and B are vectors, it returns the scalar vector product of these vectors but if the arguments are a vector and a scalar, it returns the vector muliplied by the scalar. The vector functions report intermediate results to the Script Output. You can load example scripts with the buttons at the bottom.

The mathematical functions that can be used are list below. Multiplication must be specified with a '*' symbol, 3*cos(x) not 3cos(x). Powers are specified with the 'pow' function: x³ is pow(x,3) or x**3 not x^3.
<table align='center'><tr><td><ul><li>abs(x) - absolute value</li><li>acos(x) - inverse cosine</li><li>acosh(x) - inverse hyperbolic cosine</li>
<li>asin(x) - inverse sine</li><li>asinh(x) - inverse hyperbolic sine</li><li>atan(x) - inverse tangent</li><li>atanh(x) - inverse hyperbolic tangent</li><li>cos(x) - cosine</li><li>cosh(x) - hyperbolic cosine</li>
<li>exp(x) - ex</li></ul></td>
<td><ul><li>log(x) - natural logarithm</li><li>log10(x) - base-10 logarithm</li><li>pi = 3.141592653589793</li><li>pow(x,y) - compute xy</li><li>round(x) - round to the nearest integer</li>
<li>sin(x) - sine</li><li>sinh(x) - hyperbolic sine</li><li>sqrt(x) - square root</li><li>tan(x) - tangent</li><li>tanh(x) - hyperbolic tangent</li><li>H(x) - Heaviside function = 0 for x < 0, 1 for x > 0</li></ul></td></tr></table>
 
<a href="https://lampz.tugraz.at/~hadley/physikm/script/intro/vectorscript.en.php?print">Vector functions</a> 
<table align='center'><tr><td><ul><li>cross(A,B) - cross product</li><li>dot(A,B) - scalar product of two vectors </li><li>dot(a,B) - scalar a times vector B</li><li>length(A) - length of a vector</li></ul></td><td valign="top"><ul><li>unit(A) - unit vector in direction of A</li><li>vadd(A,B) - vector addition A + B</li><li>vsub(A,B) - vector subtraction A -B</li></ul></td></tr></table>

● print(x) - Text or variables can be printed to the Script Output box with the print(x) function. Text should be put in quotes, print("Print some text"). The value of variable x can be printed with print(x) and text can be mixed with variables by concatenating them together with a + sign, print("The length is "+x+" m.").


Script Output

//The same calculations as performed on the webpage:
// http://lampz.tugraz.at/~hadley/physikm/apps/vector.en.php

A = [1,2,3];
B = [-1,3,-5];

L_A = length(A);
L_B = length(B);

print("The length of vector A is "+L_A);
print("The length of vector B is "+L_B);

AdotB = dot(A,B);
print("The scalar product A.B = "+AdotB);

theta = acos(dot(A,B)/(length(A)*length(B)));
print("The angle between A and B is "+theta+" rad.");

AcB = cross(A,B);
print("The cross product A x B = ["+AcB+"]");

sin_theta = length(cross(A,B))/(length(A)*length(B));
print("The sine of the angle between A and B is "+sin_theta);

uA = unit(A);
print("The unit vector pointing in the direction of A is ["+uA+"]");
uB = unit(B);
print("The unit vector pointing in the direction of B is ["+uB+"]");

para = dot(dot(A,uB),uB);
print("The component of A parallel to B is ["+para+"]");
perp = vsub(A,para);
print("The component of A perpendicular to B is ["+perp+"]");

AaB = vadd(A,B);
print("The vector addition A + B = ["+AaB+"]");

AsB = vsub(A,B);
print("The vector subtraction A - B = ["+AsB+"]");

BsA = vsub(B,A);
print("The vector pointing from A to B is B - A = ["+BsA+"]");

uBsA = unit(BsA);
print("The unit vector pointing from A to B is (B - A)/|B - A| = ["+uBsA+"]");