Question

Position vectors u and v have terminal points of (4, -2) and (-6, -3), respectively. Match each of the following with the resulting terminal point.

1. - u
2. 1/3 v
3. u - v
4. - 2v
5. - v - u

Options:

A) (2, 5)

B) (-4, 2)

C) (10, 1)

D) (12, 6)

E) (-2, -1)

Answer 1

To find the resulting terminal point for each operation, negate, divide or multiply the coordinates of the position vectors accordingly. Option A matches -v-u, option B matches -u, option C matches u-v, option D matches -2v, and option E matches 1/3v.

Step-by-step explanation:

To find the resulting terminal point, we need to perform the given operations on the position vectors:

1. To find -u, we simply negate the coordinates of vector u, which gives us (-4, 2). This matches option B.
2. To find 1/3v, we scale down the coordinates of vector v by dividing them by 3, which gives us (-2, -1/3). This matches option E.
3. To find u-v, we subtract the corresponding coordinates of the vectors, which gives us (4-(-6), -2-(-3)) = (10, 1). This matches option C.
4. To find -2v, we multiply the coordinates of vector v by -2, which gives us (2(-6), 2(-3)) = (-12, -6). This matches option D.
5. To find -v-u, we negate the coordinates of both vectors and then subtract the corresponding coordinates, which gives us (-(-6)-4, -(-3)-(-2)) = (2, 5). This matches option A.