Final answer:
The measure of the angle between two vectors can be found by using the cosine of the angle, which is equal to the dot product of the vectors divided by the product of their magnitudes. The angle is then obtained by taking the inverse cosine of that result.
Step-by-step explanation:
The student is attempting to find the measure of the angle between vectors. This can be accomplished using vector algebra principles, specifically by utilizing the dot product and the magnitudes of the vectors. The question gives us two vectors, vector A and vector B, and provides their magnitudes and the magnitudes of their sum and difference.
To calculate the angle, θ, between vector A and vector B, we can use the following formula derived from the dot product:
cos(θ) = (A · B) / (|A| * |B|)
Where A · B is the dot product of vectors A and B, and |A| and |B| are the magnitudes of vectors A and B, respectively. By calculating the dot product of A and B, and then dividing by the product of their magnitudes, we can find the cosine of the angle. Finally, we can obtain the angle by taking the inverse cosine of that result.
Once the angle is computed, it can be expressed in degrees using a calculator or a trigonometric table to find the inverse cosine function. This process demonstrates the use of both algebraic and analytical computation techniques in vector operations.