httpsgyazocom8ea663ad78d875091e98ac1bc111cc05 Choose any of

https://gyazo.com/8ea663ad78d875091e98ac1bc111cc05

Choose any of the four.

If you do all four, a statue will be built in your name.

Solution

1)

u=RS,v=OP

u=S-R,v=P-O

u=(2,4)-(-2,-1),v=(1,4)-(-3,-1)

u=<2-(-2) ,4-(-1)>,v=<1-(-3),4-(-1)>

u=<4 ,5>,v=<4,5>

direction and magnitude of u,v are same

so u and v are equal

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2)

u=(2,3)-(0,0)=<2,3>

v=(-3,5)-(0,0)=<-3,5>

u.v =<2,3>.<-3,5>

u.v =(2*-3)+(3*5)

u.v=-6+15

u.v=9

|u|=[2²+3²]=13 ,|v|=[(-3)²+5²]=34

cos=(u.v)_/|u||v|

cos=(9)_/13*34

cos=0.42808634473904467103117355999425

=64.654^o

angle between vectors u and v is 64.654^o

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3)

v=(6,-4)-(3,0)

v=<6-3,-4-0>

v=<3,-4>

direction angle =360^o-tan^-1(4_/3)

direction angle =360^o-53.13^o

direction angle =306.9^o

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4)

|F|=30lbs

|PQ|=80ft

=30^o

W=|F||PQ|cos

W=30*80*cos30^o

W=2078.46 lbs ft

work done pulling the wagon=2078.46 lbs ft