To find the angle between the vectors and , we can use the information given in the problem along with the properties of vectors.

Identify the Magnitudes:

The magnitudes of the vectors are given as follows:

Use the Vector Addition Formula:

According to the problem, we have:

Apply the Law of Cosines:

The Law of Cosines states that for any two vectors and , the magnitude of their resultant vector can be expressed as:

Here, is the angle between and .

Substitute the Known Values:

Plugging in the magnitudes:

This simplifies to:

Simplify the Equation:

Combine the terms on the right side:

Rearranging gives:

Solve for :

This implies:

Determine the Angle:

The angle for which is:

Final Answer:
The angle between and is .