Final answer:
The angle between vectors a and b, whose magnitudes are 3.05 and 3.03, respectively, and whose vector product is given, is about 90 degrees. Therefore, the correct option is d. 90 degrees.
Step-by-step explanation:
To determine the angle between two vectors a and b given their magnitudes and vector product, one can use the formula for the vector product (cross product) of two vectors, a × b = |a||b|sin(θ)n, where |a| and |b| are the magnitudes of vectors a and b respectively, θ is the angle between them, and n is a unit vector perpendicular to the plane containing a and b.
The magnitude of the vector product is given by |a × b| = |a||b|sin(θ). Therefore, to find the angle θ, we can rearrange this equation to solve for sin(θ) as sin(θ) = |a × b| / (|a||b|).
Given the magnitudes a = 3.05 and b = 3.03, and the vector product a × b = -5.08 k + 2.02 i, we find the magnitude of the vector product as √((-5.08)^2 + (2.02)^2) = √(27.0808) ≈ 5.2063. Substituting these values into the equation for sin(θ), we get sin(θ) = 5.2063 / (3.05 × 3.03), which gives θ ≈ 90 degrees.