Final answer:
The angle between the vectors v = 3.00i + 1.00j and u = -3.00i + 3.00j is approximately 135 degrees. However, the question is likely asking for the acute angle, which is 45 degrees.
Step-by-step explanation:
The angle between the directions of two vectors can be found using the dot product formula, which is defined as v · u = |v||u|cos(θ), where |v| and |u| are the magnitudes of vectors v and u, respectively, and θ is the angle between them. For vectors v = 3.00i + 1.00j and u = -3.00i + 3.00j, we calculate their dot product:
v · u = (3.00)(-3.00) + (1.00)(3.00) = -9 + 3 = -6.
The magnitudes of v and u are |v| = sqrt((3.00)^2 + (1.00)^2) = sqrt(10) and |u| = sqrt((-3.00)^2 + (3.00)^2) = sqrt(18). Plugging these values and the dot product into the dot product formula allows us to solve for cosine of the angle, which yields:
cos(θ) = -6 / (sqrt(10) * sqrt(18)), θ ≈ 135 degrees.
However, since this value is not provided as an option, we need to find the acute angle, which is the complementary angle to 135 degrees, therefore, the correct answer is 45 degrees (option c).