Find the components along the coordinate axes of the position vector of each of the following points –

i. P (3, 2)

ii. Q (5, 1)

iii. R (–11, –9)

iv. S (4, –3)

(i) Given P = (3, 2)

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

Let position vector of point P be.

So, component of along the X-axis is , that is a vector of magnitude 3 along the positive direction of the X-axis.

Also, component of along the Y-axis is , that is a vector of magnitude 2 along the positive direction of the Y-axis.

(ii) Given Q = (5, 1)

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

Let position vector of point Q be.

So, component of along the X-axis is 5, that is a vector of magnitude 5 along the positive direction of the X-axis.

Also, component of along the Y-axis is , that is a vector of magnitude 1 along the positive direction of the Y-axis.

(iii) Given R = (–11, –9)

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

Let position vector of point R be.

So, component of along the X-axis is , that is a vector of magnitude 11 along the negative direction of the X-axis.

Also, component of along the Y-axis is , that is a vector of magnitude 9 along the negative direction of the Y-axis.

(iv) Given S = (4, –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 vector of point S be.

So, component of along the X-axis is , that is a vector of magnitude 4 along the positive direction of the X-axis.

Also, component of along the Y-axis is , that is a vector of magnitude 3 along the negative direction of the Y-axis.