Find the vector product (expressed in unit vectors) of the two vectors given in Exercise 1.38. What is the magnitude of the vector product?

Solution 48E The two vectors are, A = 4 i + 7 j B = 5 i 2 j The cross product of two vectors is defined as, = (a b a b ) i (a b b a ) j + (a b b a ) k 2 3 3 2 1 3 1 3 1 2 1 2 = (a b b a ) k 1 2 1 2 [as the z components are all zero, because these are 2 dimensional vectors] So, A × B = [4 × ( 2) 7 × 5] k = ( 8 35)k = 43 k CONCLUSION: The magnitude of the cross product is 43. The direction is along negative z-axis.