Answer
$-24$
Work Step by Step
Let $u=\left\langle a,b\right \rangle$ and $v=\left\langle c,d\right \rangle$ be two vectors then their dot product is given by
$u\cdot v=\left\langle a,b\right \rangle \cdot \left\langle c,d\right \rangle=ac+bd$
Now for $u=\left\langle -2,1\right \rangle$ , $v=\left\langle 3,4\right \rangle$ and $w=\left\langle -5,12\right \rangle$ we have
$u\cdot v=\left\langle -2,1\right \rangle \cdot \left\langle 3,4\right \rangle$
$u\cdot v= (-2)(3)+(1)(4)=-6+4=-2$
and
$u\cdot w=\left\langle -2,1\right \rangle \cdot \left\langle -5,12\right \rangle$
$u\cdot w=(-2)(-5)+(1)(12)=10+12=22$ .
Therefore, $u\cdot v=-2$ and $u\cdot w=22$ .
Now
$u\cdot v-u\cdot w=-2-22=-24$
Hence, $u\cdot v-u\cdot w=-24$ .
