Final answer:
The y-component of vector B is found by dividing the k-component of the cross product (98) by the magnitude of vector A (125), yielding 0.784 m or 784 mm.
Step-by-step explanation:
The student is asking about the y-component of vector B given that vector A = 125i and the cross-product of vectors A and B is A × B = 98k. Since vector A is along the x-axis and vector B is perpendicular to A, vector B will not have an x-component due to their orthogonal relationship. Furthermore, the z-component of vector B must be zero because the result of the cross product is entirely in the k direction (along the z-axis).
To find the y-component of vector B, we can use the definition of the cross product for vectors in component form, which states that for vectors A = Axî + Ayâ and B = Bxî + Byâ, their cross product A × B = (AyBz - AzBy)k among other components. Here, A = 125î and A × B = 98k, which implies that the product of the magnitude of A (125) and the y-component of B must equal 98.
Therefore, to solve for the y-component of B we set up the equation 125 * By = 98, which yields By = 98 / 125. Thus, the y-component of vector B is 0.784 meters or in SI units 784 millimeters.