Final answer:
To find the magnitude of 4A where A = (6m)I - (8m)j, we calculate |4A| = √((24m)^2 + (-32m)^2) which equals 40m. However, this answer isn't among the provided choices, suggesting a typo in the question or the options.
Step-by-step explanation:
If the vector A is given by A = (6m)I - (8m)j, then to find the magnitude of 4A, we first need to multiply the vector A by 4, resulting in 4A = (24m)i - (32m)j. Next, we find the magnitude of 4A using the formula for the magnitude of a vector, which is the square root of the sum of the squares of its components.
The magnitude of 4A is |4A| = √((24m)^2 + (-32m)^2) = √(576m^2 + 1024m^2) = √1600m^2 = 40m. However, as 40m is not an option in the given choices, it seems there might be a typo in the question or options provided. None of the choices a) 4m, b) 32m, c) 48m, or d) 64m are correct.