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
Verified step by step guidance
1
Identify the components of vectors A and B. Vector A has components A_x = 4.00 and A_y = 7.00. Vector B has components B_x = 5.00 and B_y = -2.00.
Use the formula for the cross product of two vectors in two dimensions, which is given by A x B = (A_x * B_y - A_y * B_x) k. Here, k is the unit vector in the z-direction perpendicular to the xy-plane.
Substitute the components of vectors A and B into the formula: (4.00 * -2.00) - (7.00 * 5.00).
Calculate the expression inside the parentheses to find the coefficient of the unit vector k.
The magnitude of the vector product A x B is the absolute value of the coefficient obtained in the previous step.