Find the vector product A x B (expressed in unit vectors) of the two vectors given in Exercise 1.38. What is the magnitude of the vector product? Given two vectors A = 4.00 i + 7.00j and B = 5.00 i − 2.00

The vector product, or cross product, of two vectors results in a third vector that is perpendicular to the plane containing the original vectors. It is calculated using the determinant of a matrix formed by unit vectors and the components of the given vectors. The direction follows the right-hand rule, and the magnitude is given by |A||B|sin(θ), where θ is the angle between A and B.

Unit vectors are vectors with a magnitude of one, used to indicate direction in space. In Cartesian coordinates, the standard unit vectors are i, j, and k, representing the x, y, and z axes, respectively. They are essential in expressing vectors in component form, allowing for operations like addition, subtraction, and cross product to be performed algebraically.

The magnitude of a vector is a measure of its length or size, calculated using the square root of the sum of the squares of its components. For a vector resulting from a cross product, the magnitude can be found using the formula |A x B| = |A||B|sin(θ), which represents the area of the parallelogram formed by the original vectors. This is crucial for understanding the scale of the resulting vector.