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If vector u has its initial point at (-7, 3) and its terminal point at (5, -6), u = 12i + whatj? If v = -11i + 3j, 2u - v = 35i + whatj?

a. 9
b. 12
c. 15
d. 18

1 Answer

5 votes

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.

User Jan Wrobel
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