Question

Find (a) u + v,   (b) u - v,   and  (c) 2u - 3v,  Then sketch each resultant vector.

Answer 1

Step 1 : 

Definition of vector addition and scalar multiplication :

Let and be vectors and let k be a scalar.

Then the sum of u and v is the vector :

The scalar multiple of k times u is the vector :

Step 2 :

The vectors are and .

(a)

Graph of the resultant vector

Solution :

(a)

Graph of the resultant vector

Answer 2

Step 1 :

The vectors are and .

(b)

Graph of the resultant vector

Solution :

(b)

Graph of the resultant vector

Answer 3

Step 1 :

The vectors are and .

(c)

Graph of the resultant vector

Solution :

(c)

Graph of the resultant vector