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, $u \cdot v= \lt -2, 1 \gt \cdot \lt 3, 4 \gt =(-2)(3)+(1) (4)=-6+4=-2$
and $u \cdot w= \lt -2, 1 \gt \cdot \lt -5, 12 \gt =(-2)(-5)+(1) (12)=10+12=22$
$u \cdot v -u \cdot w = -2-22=-24$