def test_cross_product_anti_commutative():
vec1 = Vector([1, 2, 3])
vec2 = Vector([4, 5, 6])
vec3 = vec2.crossProduct(vec1)
assert vec3 == Vector([3, -6, 3])
assert vec1.dotProduct(vec3) == 0
assert vec2.dotProduct(vec3) == 0
def test_cross_product():
vec1 = Vector([1, 2, 3])
vec2 = Vector([4, 5, 6])
vec3 = vec1.crossProduct(vec2)
assert vec3 == Vector([-3, 6, -3])
assert vec1.dotProduct(vec3) == 0
assert vec2.dotProduct(vec3) == 0
def test_vector_dotproduct():
vec1 = Vector([2, 2])
vec2 = Vector([2, 2])
dotp = vec1.dotProduct(vec2)
assert dotp == 8
v4 = Vector([8.462, 7.893, -8.187])
w4 = Vector([6.984, -5.975, 4.778])
v5 = Vector([-8.987, -9.838, 5.031])
w5 = Vector([-4.268, -1.861, -8.866])
v6 = Vector([1.5, 9.547, 3.691])
w6 = Vector([-6.007, 0.124, 5.772])
answers = []
answers.append(round(x1 + y1, 3))
answers.append(round(x2 - y2, 3))
answers.append(round(x3.scalarMultiple(y3), 3))
answers.append(round(x4.magnitude(), 3))
answers.append(round(x5.magnitude(), 3))
answers.append(round(x6.normalise(), 3))
answers.append(round(x7.normalise(), 3))
answers.append(round(x8.dotProduct(y8), 3))
answers.append(round(x9.dotProduct(y9), 3))
answers.append(round(x10.angle(y10), 3))
answers.append(round((x11.angle(y11, in_degrees=True)), 3))
answers.append("Q1 Is parallel " + str(x12.isParallel(y12)) +
" : Is orthogonal " + str(x12.isOrthogonal(y12)))
answers.append("Q2 Is parallel " + str(x13.isParallel(y13)) +
" : Is orthogonal " + str(x13.isOrthogonal(y13)))
answers.append("Q3 Is parallel " + str(x14.isParallel(y14)) +
" : Is orthogonal " + str(x14.isOrthogonal(y14)))
answers.append("Q4 Is parallel " + str(x15.isParallel(y15)) +
" : Is orthogonal " + str(x15.isOrthogonal(y15)))
answers.append(round(v1.vProjected(b1), 3))
answers.append(round(v2.vOrthogonal(b2), 3))
answers.append(
str(round(v3.vProjected(b3), 3)) + " " +
