Interpreting a 2d vector diagram

Question

I found this question in the 3rd edition Strang Linear Algebra book. I don't understand what I'm looking at in the diagram.

I think:

1) The yellow piece is the vector W.

2) The green piece is the vector "vector V minus vector U"

3) Vector V is not shown, however I know U = 1/2V + 1/2W so V = 2U-W

4) The blue piece, a dashed line. Is it supposed to represent where the vector U could terminate on any piece of that dashed line depending on the value of V is?

Answer 1

It's surely a bug in the picture. The label $v - u$ should be just $v$. (Or else it's a VERY bad illustration, because $v-u$ and $v$ appear to almost coincide (assuming that the label for $u$ is correct), in which case $u$ must be almost zero, which it isn't in this picture.)

Answer 2

I support John's answer:

Assuming the green vector is $v - u$, a parameterization of the dotted line is $$ (1-\lambda) w + \lambda (v-u) $$ with $\lambda \in [0, 1]$.

For $\lambda = 1/2$ we would get $$ w/2 + v/2 - u/2 = u - u/2 = u/2 $$ instead of $u$.

Assuming the green vector is plain $v$, the parametrization of the dotted line would be $$ (1 - \lambda) w + \lambda v $$ and $\lambda = 1/2$ would give $w/2 + v/2 = u$, as it should.