If the force moving an object points at least partially in the opposite direction of the objects motion, the work is considered to be

If the force moving an object points at least partially in the opposite direction of the objects motion, the work is considered to be negative.

Explanation:

Work done is the measure of displacements caused on an object by the amount of force acting on it. The work done can be positive or negative. If the direction of force acting on an object is along the direction of motion of the object then the work done is positive.

This is because, in this case the external force is helping the object to continue its state of motion. So, if the force acting on the object is in completely opposite or partially opposite direction to the direction of motion of the object, it will stop or slow down the motion of the object.

This kind of force will have negative direction to the motion of the object and hence the work done will also be negative.

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