Find a geometrical description of the set of all vectors of the form av+bw where a+b=1 My first intuition for solving this problem was to solve for $a$, therefore $a = 1-b$,
and letting $v$  and $w$ be arbitrary vertices $v =(1,3)$ and  $w = (5,2)$. Since the original question is $av+bw$ I just substitute $(1-b)*(1,3)+b(5,2) = ?$ Then multiply by using the dot product, $(1,-3b) + (5b+2b)$... I'm really stuck in here, now my question is am I doing this alright? and if so what do I do next? I also though of some how relating this to a span of vectors, which is $c_1v_1+c_2v_2+c_3v_3+\ldots+c_nv_n$ And if this is the case how do I start ? Thank you in advance (:

$1-b$ is a number, there is no dot product for us to take.
$$(1-b)\cdot(1,3) + b\cdot (5,2)= (1,3) +b((5,2)-(1,3))$$
Try to simplify the expression above and think of which object is it.
