Final answer:
To find the angle between two vectors, use the dot product formula, rearrange it to solve for cos(φ), and then evaluate the inverse cosine (arcos) of this value.
Step-by-step explanation:
To find the angle between two vectors, you should use the dot product formula (also known as the scalar product). The dot product of two vectors A and B is given by the formula A · B = AxBx + AyBy + AzBz, which equals AB cos(φ), where AB represents the product of the magnitudes of vectors A and B, and φ is the angle between the vectors. To find the angle, rearrange the formula to solve for cos(φ), so cos(φ) = (A · B) / (AB). Then, calculate the angle by evaluating the inverse cosine (arcos) of this value.
The cross product, denoted by A × B, is different from the dot product and results in a vector that is perpendicular to both input vectors, with a magnitude equal to AB sin(φ). However, it is not directly used to find the angle between the vectors.
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