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Answer 1 · 2017-10-12T22:07:59

#"magnitude=47.17 units , angle=122.01"^o#

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#"let the x-component of the vector be "F_x" (it has shown as green)."#

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#"let the y-component of the vector be "F_y" (it has shown as blue)."#

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#"The F vector shows the composition of "F_x " and " F_y" (it has shown as red)".#

#"the magnitude of F vector can be calculated using the fallowing formula."#

#F=sqrt(F_x^2+F_y^2)#

#F_x=-25" , "F_y=40#

#F=sqrt((-25)^2+40^2)#

#F=sqrt(625+1600)#

#F=sqrt(2225)#

#F=47.17 " units."#

#"You need to calculate the angle "alpha " or "theta " to express direction of vector F."#

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#tan alpha=(F_y)/(F_x)#

#tan alpha=(40)/(-25)#

#tan alpha=-1.6#

#alpha=-57.99 ^o#

#"or "theta"=180-57.99=122.01^o#