Final answer:
The largest magnitude of the vector product occurs when two vectors are perpendicular, with the magnitude being the product of their magnitudes. For example, vectors with magnitudes 20 m and 6 m would have a maximum vector product magnitude of 26 m when pointing in the same direction.
Step-by-step explanation:
The largest possible value for the magnitude of the vector product â⃒ ã⃒, also known as the cross product, occurs when the two vectors are perpendicular (orthogonal) to each other. When vectors â⃒ and ã⃒ are perpendicular, their magnitudes are multiplied together along with the sine of 90 degrees (which is 1), resulting in the maximum value of their vector product. This means the magnitude of the vector product |a⃒ × b⃒| is simply |a⃒| × |b⃒|, where |a⃒| and |b⃒| are the magnitudes of the original vectors.
If we consider vectors with specific magnitudes, say A = 20 m and B = 6 m, the largest magnitude of their sum (resultant vector) would be 26 m (achieved when they point in the same direction), and the smallest magnitude would be 14 m (achieved when they point in opposite directions).