Question

For the following exercises, calculate u ⋅ v.

Given the vectors shown in Figure 4, sketch u + v, u − v and 3v.

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 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 3v by thrice the length of vector v. The graph is as follows,