Final answer:
The correct j component of vector u should be -9, and the j component of 2u - v should be -21, indicating an error in the question as none of the provided options match the calculated result.
Step-by-step explanation:
To find the vector u given its initial point at (-7, 3) and its terminal point at (5, -6), we subtract the coordinates of the initial point from the coordinates of the terminal point: (5 - (-7), -6 - 3), simplifying to (12, -9). Therefore, vector u can be written as 12i - 9j, which means u = 12i + (-9)j.
Given that v = -11i + 3j and the equation 2u - v, we can find the j component by first multiplying vector u by 2 and then subtracting vector v. So, 2u - v = 2(12i - 9j) - (-11i + 3j). This simplifies to 24i - 18j + 11i - 3j, which sums up to 35i - 21j.
Therefore, the j component of the vector 2u - v is -21, which is not one of the options provided. Based on the options, it seems there may be an error in the question as presented.