Final answer:
To find the angle between vectors mathbfa and mathbfb, use the dot product formula and the given magnitudes and dot product to solve for the angle using the inverse cosine function.
Step-by-step explanation:
The student has asked to find the angle between two vectors mathbfa and mathbfb given the magnitudes and the dot product of the vectors. To find the angle between two vectors, we can use the dot product formula:
A · B = |A| |B| cosθ
Where A · B is the dot product of vectors A and B, |A| and |B| are the magnitudes of vectors A and B, respectively, and θ is the angle between A and B. Given that A · B = 6 - √2, |A| = 3 - √2, and |B| = 2, we can rearrange the formula to solve for θ.
θ = cos⁻¹ [(A · B) / (|A| |B|)]
Therefore, θ = cos⁻¹ [(6 - √2) / ((3 - √2) × 2)]
Upon calculating the above expression, we will find the angle between vector A and vector B.