Final answer:
The magnitude of the vector product between vectors A and B is 197.12 m.
Step-by-step explanation:
The magnitude of the vector product between vectors A and B can be calculated using the formula:
A × B = |A| |B| sin(θ)
Given that the scalar product, A · B, is 71.0 m2 and the magnitudes of vectors A and B are 13.0 m and 16.0 m respectively, we can solve for sin(θ) using the equation:
A · B = |A| |B| cos(θ)
Substituting the given values into the equation, we have:
71.0 m2 = (13.0 m) (16.0 m) cos(θ)
cos(θ) = 71.0 m2 / (13.0 m × 16.0 m) = 71.0 m2 / 208.0 m2 = 0.341
Since cos(θ) = adjacent / hypotenuse, we can use the Pythagorean identity sin2(θ) + cos2(θ) = 1 to solve for sin(θ):
sin(θ) = sqrt(1 - cos2(θ)) = sqrt(1 - 0.3412) = sqrt(0.884) = 0.940
Finally, we can calculate the magnitude of the vector product:
|A × B| = |A| |B| sin(θ) = (13.0 m) (16.0 m) (0.940) = 197.12 m