Graphing a vector with components?

Hello Lilly - I will try to explain it in steps.

Firstly, v + 2w - z can be written as v + w + w - z (these are all vectors)

1. First draw your axis (x-axis, y-axis) in the middle of your graph paper

2. Start with v such that the base is at (0,0) on your graph paper. It goes 4 grids horizontally and then 2 grids vertically (I will write this as 4i + 2j)

3. At the arrow of the v vector start your w vector. Add one w vector. We know that for the W vector it goes 3 grids horizontally to the left and then goes 4 grids down. I will write this as 3i - 4j (Remember start at the arrow of the preceding vector which in this case is the v vector you drew in step 2.

4. Add to it another w vector starting from the arrow of the vector drawn in step 3. This is another w vector which can be written as 3i - 4j

5. Add to it a negative z vector. The positive z vector is just 5 grids up (written as 0i + 5j) so a negative z vector is 5 grids down.

If we add all the i's and j's we end up with.

v + w + w - z

=(4i + 2j) + (3i - 4j) + (3i - 4j) - (0i + 5j)

=4i + 3i + 3i - 0i + 2j - 4j - 4j - 5j

=10i - 11j

What this tells us is that starting from (0,0) (ie the start of the v vector) once you plot v + 2w - z you should end up at 10 grids horizontally to the right (10i) and 11 grids down (-11j)

Hope this helps, it is easier if I could draw it for you to help you learn vector addition and subtraction