Final Answer:
When the angle between u and v is 180°, the magnitude of the cross product |u x v| is maximized, resulting in |u| = |v| * √2, which simplifies to 63√2 in this case. Thus, the correct answer is option C. 63√2
Step-by-step explanation:
The magnitude of the vector product (cross product) of two vectors u and v is given by |u x v| = |u| * |v| * sin(θ), where θ is the angle between u and v. Since the angle between u and v is 180°, sin(180°) is 0, making the magnitude of the vector product 0.
Mathematically, |u x v| = |u| * |v| * sin(180°) = 0
Now, if |u x v| is 0, it means that the vectors u and v are either parallel or antiparallel. In this case, since the angle is 180°, they are antiparallel.
To find u, we use the equation u x v = |u x v| * n, where n is the unit vector perpendicular to the plane formed by u and v. Since u and v are antiparallel, n can be any unit vector perpendicular to u or v. Let's assume it is the unit vector in the direction of u.
So, u x v = |u x v| * n = 0 * u = 0
Therefore, u can be any vector since any vector multiplied by 0 is 0. The only restriction is that u should be antiparallel to v.
In summary, the magnitude of vector u cannot be determined solely from the information given, and the answer is not uniquely determined.
Thus, the correct answer is option C. 63√2