Answer:
[tex]11.18\ \text{units}[/tex]
[tex]10.3^{\circ}[/tex]
Step-by-step explanation:
[tex]w=<-6,-5>[/tex]
[tex]z=<5,-3>[/tex]
z is subtracted from w so
[tex]w-z=<-6-5,-5-(-3)>\\\Rightarrow w-z=<-11,-2>[/tex]
Magnitude is given by
[tex]\sqrt{(-11)^2+(-2)^2}=5\sqrt{5}=11.18[/tex]
The magnitude of the resulting vector is approximately [tex]11.18\ \text{units}[/tex].
The angle is
[tex]\theta=\tan^{-1}\dfrac{-2}{-11}\\\Rightarrow \theta=10.3^{\circ}[/tex]
The direction is approximately [tex]10.3^{\circ}[/tex]