Question

An object is moved from (-2,-1,4) to (-2,3,7) with a 9N force acting in the direction of (1,1,1). Calculate the work done, The distance is in metres.

Work = |F| |d| costheta

F and d are vectors.

Answer 1

You have to obtain the unitary vector for the direction especified by the two points:
u = ((-2,3,7) - (-2,-1,4))/|| (-2,3,7) - (-2,-1,4) || (type this expression in WolframAlpha)
u = (0, 4/5, 3/5) and the distance between them: d = || (-2,3,7) - (-2,-1,4) || = sqrt((-2 -(-2))² + (3 - (-1))² + (7 - 4)²) = 5
Take the unit vector in the (1, 1, 1) direction: v = (1, 1, 1)/ || (1, 1, 1) || = (1/sqrt(3), 1/sqrt(3), 1/sqrt(3)).
To solve the problem, use W = F dot d = (9 N) v dot (5 m) u = 45 v dot u joules = 21 sqrt(3) J aprox. 36.4 J
Type 45 times (0, 4/5, 3/5) dot (1/sqrt(3), 1/sqrt(3), 1/sqrt(3)) in WolframAlpha to get this.