Question

Use the vectors in the figure at the right to graph each of the following vectors.

$2u-3v+w$

Short answer

The graph is

Step-by-step solution

Step 1. Given Information 

We are given three vectors $u,v,w$ and we need to graph the vector $2u-3v+w$.

Step 2. Plotting the graph  

At first, we find out the vector $2u$which is twice the magnitude of vector $u$.

Next we find the vector $-3v$which has magnitude thrice the vector $v$and a director opposite to the vector $v$.

So, we join the terminal point of $2u$with the initial point of vector $-3v$.

Then we add the vector $w$by joining the terminal point of vector $-3v$with the initial point of vector $w$.

The resultant vector $2u-3v+w$is obtained by joining the initial point of vector $2u$with the terminal point of vector $w$.

The graph of the resultant vector is