Vector Operations

The vector object has the properties of 3D vectors in math and science.

r = vector(x,y,z) or r=vec(x,y,z) produce the 3D vector < x, y, z >.

Vector Addition and Subtraction

a = vector(1,2,3)
b = vector(10,20,30)
print(a+b)    # displays < 1, 22, 33 >

Scalar Multiplication

a = vector(1,2,3)
c = 2*a
print(c)   # displays < 2, 4, 6 >

Magnitude

mag can be invoked as a function or an attribute:

a = vector(1,2,3)
b = vector(10,20,30)
d = mag(a)
print(d)    # displays 3.74166
e = b.mag
print(e)    # displays 37.4166

Unit Vector

There are two names for the function that calculates a unit vector: hat() and norm(). Both can be invoked as functions or attributes:

a = vector(1,2,3)
b = vector(10,20,30)
f = hat(a)
print(f)  # displays < 0.267261, 0.534522, 0.801784 >
g = norm(a)
print(g)  # displays < 0.267261, 0.534522, 0.801784 >

h = a.hat
i = b.norm

For convenience, hat( vec(0,0,0) ) = vec(0, 0, 0) to avoid runtime errors.

Dot Product

Both dot and cross products can be invoked as functions or attributes:

a1 = vector(3,1,0)
b1 = vector(0,2,0)
j = dot(a,b)
print(j)   # displays 2
k = cross(a,b)
print(k)   # displays < 0, 0, 6 >

m = a1.dot(b1)
n = a1.cross(b1)

Angle Between Vectors

The diff_angle() function returns the angle between two vectors in radians:

a1 = vector(3,1,0)
b1 = vector(0,2,0)
p = diff_angle(a1,b1)
print(p)  # displays 1.24905

q = a1.diff_angle(b1)

Projections

For convenience, the proj() function calculates the vector projection of one vector onto another:

A = vector(3,1,0)
B = vector(0,2,0)
C = proj(A,B)
print(C)   # displays < 0, 1, 0 >

Note that proj(A,B) = dot( A, hat(B) ) * hat(B)

The comp() function calculates the scalar projection of A along B:

A = vector(3,1,0)
B = vector(0,2,0)
C = comp(A,B)
print(C)   # displays 1.

Note that comp(A,B) = dot( A, hat(B) )

Random Vector

vector.random() produces a vector whose components are random numbers in the range -1 to +1.

Rotating a Vector

myvec2 = rotate( myvec1, angle=a, axis=vector(x,y,z) )

Parameters:

• firstargument (vector) – Vector to be rotated (myvec1 in example above).

• angle (scalar) – Angle of rotation in radians.

• axis (vector) – Axis of rotation. Default < 0, 0, 1 >.