
If you're new to Python A VPython tutorial Pictures of 3D objects 
The vector ObjectThe vector object is not a displayable object but is a powerful aid to 3D computations. Its properties are similar to vectors used in science and engineering. vector(x,y,z) This creates a 3D vector object with the given components x, y, and z. Vectors can be added or subtracted from each other, or multiplied by an ordinary number. For example, v1 = vector(1,2,3) You can refer to individual components of a vector: v2.x is 10, v2.y is 20, v2.z is 30 It is okay to make a vector from a vector: vector(v2) is still vector(10,20,30). This is a convenient way to make a separate copy of a vector. Vector functions The following functions are available for working with vectors: mag(A) = A.mag = A, the magnitude of a vector mag(A) # calculates length of A It is possible to reset the magnitude or the magnitude squared of a vector: v2.mag = 5 # sets magnitude to 5; no change in direction You can reset the magnitude to 1 with norm(): norm(A) # A/A, normalized; magnitude of 1 You can also write v1.norm() or v1.hat. You can change the direction of a vector without changing its magnitude: v2.hat = v1 # changes the direction of v2 to that of v1 To calculate the angle between two vectors (the "difference" of the angles of the two vectors). diff_angle(v1,v2) You can also write v1.diff_angle(v2). For convenience, if either of the vectors has zero magnitude, the difference of the angles is calculated to be zero. cross(A,B) or A.cross(B) gives the cross product of two vectors, a vector perpendicular to the plane defined by A and B, in a direction defined by the righthand rule: if the fingers of the right hand bend from A toward B, the thumb points in the direction of the cross product. The magnitude of this vector is equal mag(A)*mag(B)*sin(diff_angle(A,B)). dot(A,B) or A.dot(B) gives the dot product of two vectors, which is an ordinary number equal to mag(A)*mag(B)*cos(diff_angle(A,B)). If the two vectors are normalized, the dot product gives the cosine of the angle between the vectors, which is often useful. Rotating a vector There is a function for rotating a vector: v2 = rotate(v1, angle=a, axis=vector(x,y,z)) The angle must be in radians. The default axis is (0,0,1), for a rotation in the xy plane around the z axis. There is no origin for rotating a vector. You can also write v2 = v1.rotate(angle=a, axis=vector(x,y,z)). There is also a rotate capability for objects. There are functions for converting between degrees and radians, where there are 2*pi radians in 360 degrees: radians(360) is equivalent to 2*pi degrees(2*pi) is equivalent to 360 
