How to find work done in exact values?

[haiku11]

10N force acting in the direction of the vector (1, 1) moves an object from P (-2, 1) to Q (5, 6), calculate the work done.

The Attempt at a Solution

I can do this question correctly except I only know how to do it using decimals but the answer is in exact values of 60√2J. I can't figure out how to subtract the angle of the displacement from the angle of the force in exact values because I'll end up multiplying the force and displacement by cos (cos^-11/√2 - cos^-17√74) which I've never done before. I just found out that cos (cos^-1x) is x but that doesn't quite work if there's an addition or subtraction involved.

 

[gneill]

Work is f.d, where f and d are vectors and the "." represents the dot product. The dot product can be calculated as |f||d|cos(θ), or you can work from the definition of the dot product which operates directly on the components of the vectors:

$$\vec f \cdot \vec d = f_x d_x + f_y d_y$$

Can you write both vectors f and d in component form?

Hint: Note that the force vector has a magnitude of 10N, so it may be simplest to write it as its magnitude multiplied by a unit vector in the appropriate direction.