Hello,

I am having trouble understanding vectors. I have attempted all of the questions and the results I ended up withseem(at least to me) like they could be correct. If someone could look over what I've got and tell me if I'm on the right track I would appreciate it. The upcoming lessons build on this stuff so I need to make sure I understand it. I apologize for the quality of the images.

For this one I have the following:

a) $\displaystyle \overrightarrow{EF} - \overrightarrow{FG} = \overrightarrow{EG}$

b) $\displaystyle \overrightarrow{EF} - \overrightarrow{FG} = \overrightarrow{EF} - \overrightarrow{EH} = \overrightarrow{FH}$

c) $\displaystyle \overrightarrow{FE} - \overrightarrow{FG} = \overrightarrow{EG}$

d) $\displaystyle \overrightarrow{FG} - \overrightarrow{EF} = \overrightarrow{FG} - \overrightarrow{GH} = \overrightarrow{FH}$

The second question asks:

The diagram below shows a cube, where $\displaystyle \overrightarrow{AB} = \overrightarrow{u}$, $\displaystyle \overrightarrow{AD} = \overrightarrow{v}$ and $\displaystyle \overrightarrow{AE} = \overrightarrow{w}$. Determine a single vector equivalent to each of the following.

a) u + v + w

b) u + v - w

c) u - v + w

d) u - v - w

For this I have:

a) $\displaystyle \overrightarrow{AB} + \overrightarrow{AD} + \overrightarrow{AE} = \overrightarrow{BD} - \overrightarrow{AE} = \overrightarrow{BD} + \overrightarrow{DH} = \overrightarrow{BH}$

b) $\displaystyle \overrightarrow{AB} + \overrightarrow{AD} - \overrightarrow{AE} = \overrightarrow{BD} - \overrightarrow{AE} = \overrightarrow{BD} - \overrightarrow{BF} = \overrightarrow{DF}$

c) $\displaystyle \overrightarrow{AB} - \overrightarrow{AD} + \overrightarrow{AE} = \overrightarrow{BD} + \overrightarrow{AE} = \overrightarrow{BD} + \overrightarrow{DH} = \overrightarrow{BH}$

d) $\displaystyle \overrightarrow{AB} - \overrightarrow{AD} - \overrightarrow{AE} = \overrightarrow{BD} - \overrightarrow{AE} = \overrightarrow{BD} - \overrightarrow{BF} = \overrightarrow{DF}$

Thank you.