Which of the following displacement vectors (if any) are equal?

Variable	magnitude	direction
$\overrightarrow{\mathrm{A}}$	$100 \mathrm{m}$	$30°$ north of east
$\overrightarrow{\mathrm{B}}$	$100 \mathrm{m}$	$30°$ south of west
$\overrightarrow{\mathrm{C}}$	$100 \mathrm{m}$	$60°$ east of north

 

Consider the following four force vectors:

(a) ${\overrightarrow{F}}_1=50.0 \mathrm{N}$, due east

(b) ${\overrightarrow{F}}_2=10.0 \mathrm{N}$, due east

(c) ${\overrightarrow{F}}_3=40.0 \mathrm{N}$, due west

(d) ${\overrightarrow{F}}_4=30.0 \mathrm{N}$, due west

Which two vectors add together to give a resultant with the smallest magnitude and which two vectors add to give a resultant with the largest magnitude? In each case, specify the magnitude and direction of the resultant.

A car is being pulled out of the mud by two forces that arc applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the $90°$ angle. The magnitude of the force applied by each rope is $2000 \mathrm{N}$. Arrange the force vectors tail to head and use the graphical technique to answer the following questions:

How would the single rope be directed relative to the dashed line?

A car is being pulled out of the mud by two forces that are applied by the two ropes shown in the drawing. The dashed line in the drawing bisects the ${90}^0$ angle. The magnitude of the force applied by each rope is $2000 \mathrm{N}$. Arrange the force vectors tail to head and use the graphical technique to answer the following questions:

(a) How much force would a single rope need to apply to accomplish the same effect as the two forces are added together?

(b) How would the single rope be directed relative to the dashed line?