The angle between two vectors A and B can be determined using the concept of vector subtraction. Given that the resultant vector R is equal to A - B, we can find the angle between A and B by analyzing the properties of vector subtraction and applying trigonometry.

1. Understanding Vector Subtraction:
Vector subtraction involves subtracting the individual components of one vector from the corresponding components of another vector. In this case, we have A - B, which means we subtract the components of vector B from the components of vector A.

2. Finding the Magnitude of the Resultant Vector:
To determine the angle between A and B, we need to find the magnitude of the resultant vector R. The magnitude of a vector can be calculated using the Pythagorean theorem, which states that the square of the magnitude is equal to the sum of the squares of its components.

3. Calculating the Magnitude of R:
To find the magnitude of R, we need to square and add the components of A and B. Mathematically, it can be represented as:
|R|² = (A_x - B_x)² + (A_y - B_y)² + (A_z - B_z)²

4. Calculating the Angle between A and B:
Once we have the magnitude of R, we can use trigonometry to find the angle between A and B. The angle can be determined using the formula:
cosθ = (A · B) / (|A| * |B|)
where · represents the dot product of A and B, and |A| and |B| represent the magnitudes of vectors A and B, respectively.

5. Applying the Formula:
By substituting the values of A, B, and R, we can calculate the angle between A and B using the formula mentioned above. The dot product of A and B can be calculated by multiplying their corresponding components and summing them.

6. Obtaining the Angle:
Finally, the angle between A and B can be found by taking the inverse cosine (arccos) of the value obtained in step 5. The inverse cosine function will provide the angle in radians, which can be converted to degrees if required.

By following these steps, we can determine the angle between vectors A and B using the given information. Remember to apply the appropriate trigonometric functions and formulas to obtain an accurate result.

Magnitude
R^2= A^2+B^2-2ABcos#
A^2+B^2+2AB=A^2+B^2-2ABcos#(R=A+B)
2AB=-2ABCOS#
COS#=-1=COS 180
#=180