2 vectors what third vector is needed to counter bakance the first 2?

[calc3varbrg9e]

Homework Statement

in the given figure, vectors u and v each have a magnitude of 55 pounds. Find the magnitude and direction of the force w needed to counterbalance u and v? So the "figure" is pretty simple... it shows a line labled North and south and vector u is pointing 45 degrees in the south west direction and vector v is pointing 60 degrees in the south east direction.

Homework Equations

trig functions

The Attempt at a Solution

this is a calc3 class using the varberg 9e textbook and the class uses an online program called math lab which is provided by the textbook and therefore all the online material directly relates to the text... So I am on chapter 11 dealing with vectors... Specifically 3D vectors... however this appears to be a 2D problem... i missed a problem similar to this on my online quiz... so i went to the online practice problems and found this problem... and i clicked the "help me solve this" button which takes you step by step to the solution... At this point i could see where i made mistakes in solving the quiz problem, but i don't understand why i was wrong so my first question is... They come up with 67 pounds and so did i but they claim its at 277.5 degrees? or S7.5 degrees E? Why? wouldn't it be in the north east direction?

 

[Delphi51]

Some things aren't clear. What does "vector v is pointing 60 degrees in the south east direction" mean? Maybe 60 degrees east of south? Or 60 degrees south of east?

"they claim its at 277.5 degrees? or S7.5 degrees E?"
277 degrees is probably measured clockwise from north, so it is 360-277 = 83 degrees west of north. I don't see how it could be S 7.5 E.

 

[calc3varbrg9e]

Regardless of being east of south or south of east... i don't see how it can be S 7.5 E... Which was my question... however... it is east of south... and therefore i don't see how it can be 277.5 degrees... because the answer i come up with is 82.5 degrees north of east or of course that would be the same as 7.5 degrees east of north... so if you go clockwise 7.5+270=277.5 degrees which is their answer? that makes no sense... that's starting due east and measuring 277.5 degrees counter clockwise to the vector w...

 

[calc3varbrg9e]

the only way i have been able to see it would be for it to the resultant vector of u and v... which would be 7.5 degrees east of south... and 277.5 degrees if starting at due east and measuring counter clockwise around to the resultant vector... just like you would normally measure degrees... but that's not what they asked for? right? it should directly opposite... i would think...

 

[calc3varbrg9e]

or am i missing something? is this actually 3D? is north coming out of the page? and u and v are on the page? i wouldn't even know how to think about that?

 

[calc3varbrg9e]

they say u=<-55sin45,-55cos45> i understand
u=<-38.89,-38.89> i understand
v=<55sin60,-55cos60> i understand
v=<47.63,-27.50> i understand
u+v=<8.74,-66.39> i understand
w=-(u+v) i understand
w=<-8.74,66.39> i understand
||w||=67 pounds (i understand)

then inverse tan (66.39/-8.74)= 277.5 degrees (i don't understand)

(am i missing something?)

 

[SammyS]

277.5° is co-terminal with -82.5° (as measured from the positive x axis).

That's correct for the resultant of u+v, but w = -(u+v), so w is 180° from u+v .