Final answer:
The dot product can be used to find the angle between two vectors by using the equation Ả B = |A| |B| cos(θ). Rearrange the equation to solve for θ by taking the inverse cosine of (Ả B / (|A| |B|)). Substitute the values of the dot product and magnitudes of the vectors into the equation to find the angle.
Step-by-step explanation:
The dot product can be used to find the angle between two vectors by using the equation Ả B = |A| |B| cos(θ), where Ả B is the dot product of vectors A and B, |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
To find the angle θ, we can rearrange the equation to θ = cos-1(Ả B / (|A| |B|)). Calculate the dot product by multiplying the corresponding components of the vectors and then substitute the values into the equation to find the angle.
For example, if vectors A = [2, 3] and B = [4, 1], the dot product is 2*4 + 3*1 = 11. The magnitudes of A and B are |A| = sqrt(22 + 32) = sqrt(13) and |B| = sqrt(42 + 12) = sqrt(17). Substituting these values into the equation, we get θ = cos-1(11 / (sqrt(13) * sqrt(17))), which can be approximated to the nearest degree using a calculator.