(a)

The initial and terminal points of a vector v is and .

Graph :

(1) Draw the coordinate plane.

(2) Plot the initial and terminal points.

(3) Connect the plotted points.

Arrow indicates the direction of the vector from the initial point.

(b)

If and  are the initial and terminal points then the component form of a vector is

.

Where and are the components of the vector.

The components of the vector is

The component form of a vector is .

(c)

The linear combination of the vector is .

The linear combination of the vector is .

(d)

Graph :

(1) Draw the coordinate plane.

(2) Plot the initial point at origin and vector .

(3) Connect the plotted points.

Arrow indicates the direction of the vector from the origin.

(a) Graph of the directed line segment from initial point to terminal point :

(b) The component form of a vector is .

(c) The linear combination of the vector is .

(d) Graph of the vector from initial point at the origin :