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How to find the angle between two vectors?

A) Use the dot product formula
B) Apply the cross product formula
C) Evaluate the inverse cosine
D) Find the magnitude of each vector

User Lavita
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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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User D Ta
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