Question

Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>.

-u – v =
u – v =
v – u =

*options*
<-10,-3>
<6,-11>
<-6,11>
<10,3>

Answer 1

`-\vec{u}-\vec{v}=<6,\ -11>\\\vec{u}-\vec{v}=<-10,\ -3>\\\vec{v}-\vec{u}=<10,\ 3>`

Explanation:

`\vec{a}=<x_1,\ y_1>,\ \vec{b}=<x_2,\ y_2>\\\\\vec{a}-\vec{b}=<x_1-x_2,\ y_1-y_2>\\\\-\vec{a}=<-x_1,\ -y_1>`

-----------------------------------------------------------------------------

`-\vec{u}-\vec{v}=-<-8,\ 4>-<2,\ 7>=<-(-8),\ -4>-<2,\ 7>\\=<8-2,\ -4-7>=<6,\ -11>\\\\\vec{u}-\vec{v}=<-8,\ 4>-<2,\ 7>=<-8-2,\ 4-7>=<-10,\ -3>\\\\\vec{v}-\vec{u}=<2,\ 7>-<-8,\ 4>=<2-(-8),\ 7-4>=<10,\ 3>`

You could use

`\vec{v}-\vec{u}=-(\vec{u}-\vec{v})=-<-10,\ -3>=<-(-10),\ -(-3)>\\=<10,\ 3>`