Final answer:
In order to find the angle between two vectors, use the equation ε = cos-1((Ax * Bx + Ay * By + Az * Bz)/(AB)). Calculate the magnitude of each vector, find the dot product of the vectors, then use the inverse cosine function to find the angle.
Step-by-step explanation:
In order to determine the angle between two vectors, the equation ε = cos-1((Ax * Bx + Ay * By + Az * Bz)/(AB)) is employed.
Here, Ax, Ay, Az, Bx, By, and Bz denote the components of vectors A and B, while AB represents the product of the magnitudes of vectors A and B.
Taking vectors A = (2, -3, 5) and B = (4, 1, -2) as an example, the process unfolds as follows:
Calculate AB = sqrt((2)² + (-3)² + (5)²) * sqrt((4)² + (1)² + (-2)²) = sqrt(38) * sqrt(21).
Compute the dot product of vectors A and B: Ax * Bx + Ay * By + Az * Bz = (2 * 4) + (-3 * 1) + (5 * -2) = 8 - 3 - 10 = -5.
Substitute the values into the formula: ε = cos-1(-5/(sqrt(38) * sqrt(21))).
Calculate the angle using a calculator or trigonometric table.
Hence, the angle between vectors A and B is approximately ε = cos-1(-5/(sqrt(38) * sqrt(21))).
Complete Question:
How we find the angle between two vectors.