Answer
$-24$
Work Step by Step
Our aims is to compute the dot product , for this we will multiply the corresponding components together and then add.
In general, we have the formula as: $ \lt a , b\gt \cdot \lt c, d \gt =ac+bd$
We have: $u=\lt -2, 1 \gt $ and $v = \lt 3, 4 \gt $ and $w= \lt -5, 12 \gt $
Now, $v-w= \lt 3, 4 \gt - \lt -5, 12 \gt =\lt 3+5, 4, -12 \gt = \lt 8, -8 \gt $
Therefore,
$u \cdot (v-w) = \lt -2, 1 \gt \cdot \lt 8, -8 \gt \\= (-2)(8) +(1)(-8) \\= -16-8 \\=-24$