The vector is .

The scalar multiple of  and    is the vector .

(a)

Find .

The scalar multiple of 2 and v is the vector

Graph :

(1) Draw the coordinate plane.

(2) Plot the vectors v and .

(3) Connect the plotted vectors.

Here 2 is positive, has the same direction as v.

(b)

Find .

The scalar multiple of  and v is the vector

Graph :

(1) Draw the coordinate plane.

(2) Plot the vectors v and .

(3) Connect the plotted vectors.

Here is negative, has the opposite direction.

(c)

Find .

The scalar multiple of and v is the vector

Graph :

(1) Draw the coordinate plane.

(2) Plot the vectors v and .

(3) Connect the plotted vectors.

Here is positive, has the same direction as v.

(d)

Find .

The scalar multiple of and v is the vector.

Graph :

(1) Draw the coordinate plane.

(2) Plot the vectors v and .

(3) Connect the plotted vectors.

Here is positive, has the same direction as v.

(a) .

Graph of the scalar multiple of :

(b) .

Graph of the scalar multiple of :

(c) .

Graph of the scalar multiple of :

(d) .

Graph of the scalar multiple of :