Script Example: Calculate the angle between two vectors

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>asin(x) - inverse sine</li><li>atan(x) - inverse tangent</li><li>cos(x) - cosine</li>
<li>exp(x) - et</li><li>log(x) - natural logarithm</li></ul></td>
<td><ul><li>pi = 3.141592653589793</li><li>pow(t,y) - compute ty</li><li>round(x) - round to the nearest integer</li>
<li>sin(x) - sine</li><li>sqrt(x) - square root</li><li>tan(x) - tangent</li><li>H(x) - Heaviside function = 0 for x < 0, 1 for x > 0</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.").

In this example, a script will be written to calculate the angle between two vectors $\vec{A}= 3\,\hat{x} -5 \,\hat{y} +7\,\hat{z}$ and $\vec{B}= -2\,\hat{x} +6 \,\hat{y} +9\,\hat{z}$. The scalar product of these two vectors is,

$$\vec{A}\cdot\vec{B} = A_xB_x + A_yB_y + A_zB_z = |\vec{A}||\vec{B}|\cos\theta,$$

Where $\theta$ is the angle between the vectors. The script solves for the angle $\theta$.

//calculate the angle between vectors A and B Ax = 3; // x component of vector A Ay = -5; // y component of vector A Az = 7; // z component of vector A Bx = -2; // x component of vector B By = 6; // y component of vector B Bz = 9; // z component of vector B //calculate the scalar product AdotB = AxBx + AyBy + AzBz; print("The scalar product is:"); print(AdotB); print(" "); //calculate the length of vector A length_A = sqrt(AxAx + AyAy + AzAz); print("The length of vector A is:"); print(length_A); print(" "); //calculate the length of vector B length_B = sqrt(BxBx + ByBy + BzBz); print("The length of vector B is:"); print(length_B); print(" "); //calculate the angle between vectors A and B cos_theta = AdotB/(length_Alength_B); theta = acos(cos_theta); print("The angle between vectors A and B is: "+theta+" rad.");
Script Output






	Physik M 513.805 (511.015)