Calculus problem?

Question

If anyone could explain how the following problem is done, it would be greatly appreciated.

In the following problem, find the work W done by the force F in moving a particle in a straight line from P to Q:

F = i - k
P(0, 0, 0), Q(3, 1 , 0)

Answer 1

That's more a physics problem than calculus, isn't it?

Work is force times distance. You need to calculate the dot-product of the force vector and the distance vector.

Since P and Q have the same z-value (k unit vector), the "-k" can be ignored, and the dot-product of i and PQ is just the difference in their x-values.

My answer would be 3, but I'm a little rusty on the physics.

Answer 2

Distance vector d = (3**1**0)
Force vector = (1**0**-1)
Work done = F • d = (3 x 1) + (1 x 0) + (0 x - 1)
F • d = 3
Work done = 3

Answer 3

First you find the displacement vector: PQ = (3-0)i + (1-0)j +(0-0)k = 3i + j

Now, the work W = F.PQ

W =(1,0,-1).(3,1,0) = 3+ 0+0 = 3

Answer 4

WD - work done.
d - distance.
F - Force.

d = √(3² + 1²)
d = √(10)

WD = F*d
WD = F*√(10)
WD = (i - k)*√(10)
WD = (√10)i - (√10)k