This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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The vector product (or cross product) of two vectors A and B is a vector C that is perpendicular to both A and B. Its magnitude is given by |A||B|, where is the angle between them. Mathematically, if A = A_xi + A_yj + A_zk and B = B_xi + B_yj + B_zk, their cross product is calculated as the determinant: A × B = i & j & k \\ A_x & A_y & A_z \\ B_x & B_y & B_z = (A_yB_z - A_zB_y)i - (A_xB_z - A_zB_x)j + (A_xB_y - A_yB_x)k In mathematical analysis, the vector product is fundamental in vector calculus for defining quantities such as torque and angular momentum, and it is essential for differentiating vector functions, where the product rule for cross products applies: (d)/(du)(A × B) = A × dBdu + dAdu × B. Got more? Send 'em.