Final answer:
The angle in radians between two vectors can be found using the dot product and magnitudes of the vectors; by taking the arccos of the dot product divided by the magnitude's product, the angle in radians is obtained, which ranges from 0 to π.
Step-by-step explanation:
To find the angle in radians between the vectors u and v, you can use the dot product formula which is defined as u · v = |u| |v| cos(θ), where |u| and |v| are the magnitudes of the vectors and θ is the angle between them. By rearranging this formula, we can solve for the angle by taking the inverse cosine (also known as arccos) of the dot product of u and v divided by the product of the magnitudes of u and v.
First, compute the dot product of the vectors. Then, calculate the magnitudes of each vector. Finally, divide the dot product by the product of the magnitudes, and take the inverse cosine of the result to get the angle in radians.
It's important to note that angles are commonly defined as positive in the counter clockwise direction. Additionally, the range of the arccos function is from 0 to π radians, which corresponds to angles between 0° and 180°.