Question

Use the figure to graph each of the following:

$2u+3v$

Short answer

Graph is :

Step-by-step solution

Step 1. Given information 

We have been given a figure.

We have to graph $2u+3v$using the figure.

Step 2. Draw the resulting vector

We know that when we multiply a vector by a scalar we obtain another vector with the same direction but with a different magnitude (length of the vector), if the scalar is negative, the sense also changes, so to find 2u + 3v we have to draw the resulting vectors u and v as shown in the figure:

Step 3. 

Now we need to move the starting point of 3v towards the ending point of 2u, preserving the magnitude and direction of the vector, Finally, we join the initial point of 2u with the final point of 3v and obtain 2u