Question

For the following exercises, use the vectors shown to sketch u + v, u − v, and 2u.

Answer 1

Consider the graph given in the exercise.

 

Two vectors u and v are shown in the graph.

 

Compute u + v by drawing vector v from the terminal point of vector u. The new vector that begins at the initial point of u and stops at the end point of v gives the resultant vector u + v.

 

The graph of the vector u + v is as follows,

 

Compute u - v by reversing the direction of vector v and starts it from the terminal point of vector u. The new vector that begins at the initial point of u and stops at the end point of -v gives the resultant vector u - v.

 

The graph is as follows,

 

Compute 2u by twice the length of vector u. The graph is as follows,