A 127.6 N carton is pulled up a frictionless baggage ramp inclined at 30.0 ∘ above the horizontal by a rope exerting a 79.0 N pull parallel to the ramp's surface. The carton travels 6.95 m along the surface of the ramp. Calculate the work done on it by the rope, gravity, and the normal force of the ramp.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west

it was given as a lesson and guide for prayer.