What is the magnitude of the cross product of a vector of magnitude 2.00 m pointing east and a vector of magnitude 4.00 m pointing 30.0° west of north?
A) 6.93
B) -6.93
C) 4.00
D) -4.00
E) 8.00

Question

Quizplus · Accepted Answer

The magnitude of the cross product of two vectors is given by |A x B| = |A||B|sin(θ), where |A| and |B| are the magnitudes of the vectors, and θ is the angle between them. Here, the angle between the eastward vector and the vector pointing 30° west of north (which is 60° east of north) is 90° + 30° = 120°. Thus, |A x B| = 2 * 4 * sin(120°) = 8 * (√3/2) = 4√3 ≈ 6.93.

What Is the Magnitude of the Cross Product of a Vector