(i) Given A = (4, –1) and B = (1, 3)

We know position vector of a point (x, y) is given by, where and are unit vectors in X and Y directions.

Let position vectors of points A and B be and respectively.

We also have.

Recall the vector is given by

Recall the magnitude of the vector is given as

Here, x = –3 and y = 4

Thus, and.

(ii) Given A = (–6, 3) and B = (–2, –5)

We know position vector of a point (x, y) is given by, where and are unit vectors in X and Y directions.

Let position vectors of points A and B be and respectively.

We also have.

Recall the vector is given by

Recall the magnitude of the vector is given as

Here, x = 4 and y = –8

Thus, and.