Without drawing, find the resultant vectors for the following points: A) A(2,1) and B(3,-11) B) P(5,1) and Q(3,-11)

A)
To find the resultant vector for points A(2,1) and B(3,-11), we need to add the x-components and the y-components separately.

For the x-component:
2 + 3 = 5

For the y-component:
1 + (-11) = -10

Therefore, the resultant vector for points A(2,1) and B(3,-11) is R(5,-10).

B)
To find the resultant vector for points P(5,1) and Q(3,-11), we need to add the x-components and the y-components separately.

For the x-component:
5 + 3 = 8

For the y-component:
1 + (-11) = -10

Therefore, the resultant vector for points P(5,1) and Q(3,-11) is R(8,-10).

A)
```
AB = B - A =
(3, -11) - (2, 1) =
(3 - 2, -11 - 1) =
(1, -12)
```
B)
```
PQ = Q - P =
(3, -11) - (5, 1) =
(3 - 5, -11 - 1) =
(-2, -12)
```