To find the magnitude of the cross product of a force vector with another vector (in this case, the radius vector), you can use the formula:
|A x B| = |A| * |B| * sin(θ)
Where:
|A x B| is the magnitude of the cross product.
|A| is the magnitude of vector A.
|B| is the magnitude of vector B.
θ is the angle between vectors A and B.
In this case, you have the force vector F = 2i + j + 2k and the radius vector (let's call it R). The angle between the force vector and the radius vector is given as 30 degrees.
First, calculate the magnitudes of the vectors:
|F| = √(2^2 + 1^2 + 2^2) = √9 = 3
|R| = |RADIUS| (This value is not provided in the question, so you need to know the magnitude of the radius vector.)
Given that the angle θ = 30 degrees, you need to convert it to radians (since trigonometric functions typically work with radians):
θ_rad = 30 degrees * (π / 180) ≈ 0.5236 radians
Now you can plug these values into the formula to find the magnitude of the cross product:
|F x R| = |F| * |R| * sin(θ_rad)
= 3 * |R| * sin(0.5236)
The magnitude of the cross product |F x R| depends on the magnitude of the radius vector, which is missing in the provided information. If you have the magnitude of the radius vector, you can substitute it into the equation to get the final result.