Final answer:
To find the angle between the vectors A and B, use the dot product formula. The angle between the vectors A and B is approximately 42.6°.
Step-by-step explanation:
To find the angle between the vectors A and B, we can use the dot product formula:
A · B = |A| |B| cos(θ)
where A · B is the dot product, |A| is the magnitude of vector A, |B| is the magnitude of vector B, and θ is the angle between the two vectors.
In this case, A = (-2.3, 1.3) and B = (-2, 1). We can calculate their magnitudes and the dot product:
|A| = sqrt((-2.3)^2 + (1.3)^2) = 2.65
|B| = sqrt((-2)^2 + (1)^2) = 2.24
A · B = (-2.3)(-2) + (1.3)(1) = 6.39
Now we can solve for the angle θ:
6.39 = 2.65 * 2.24 * cos(θ)
cos(θ) = 6.39 / (2.65 * 2.24) = 1.5
θ = acos(1.5) ≈ 42.6°
Therefore, the angle between the vectors A and B is approximately 42.6°. The correct answer is option a.