The formula for finding the angle between vectors A and B using radians is θ = arccos((A·B) / (|A|·|B|)), where θ is the angle between the two vectors, A·B is the dot product of vectors A and B, and |A| and |B| are the magnitudes of vectors A and B, respectively.
The angle between vectors A and B is typically given in radians if the formula used is θ = arccos((A·B) / (|A|·|B|)). However, if the formula used is θ = cos-1((A·B) / (|A|·|B|)), then the angle will be in degrees.
No, the angle between vectors A and B cannot be greater than 180 degrees. This is because the range of arccosine (or cos-1) function is limited to 0 to 180 degrees, or 0 to π radians.
The dot product of vectors A and B represents the magnitude of vector A multiplied by the magnitude of the component of vector B that is parallel to vector A. This can also be interpreted as the projection of vector B onto vector A.
Yes, this formula can be extended to find the angle between multiple vectors. To do this, you can use the dot product of the first two vectors and then continue multiplying by the cosine of the angle between each subsequent vector and the resulting vector. However, this method may become more complicated and it is often easier to visualize and solve for the angles using other methods, such as drawing a diagram or using trigonometric identities.