Question

Find the work done by f along the line from points (1,2,3)to(3,5,7)where f(x,y,z) =x3i+yj+zkis the force field

Answer 1

Given: The two points (1, 2, 3) and (3, 5, 7)

To find: The work done by F along the line of points given?

Solution:

• So now we have given two points, so object in moving from point let say P(1, 2, 3) and Q(3, 5, 7).

• The position vectors will be:

                 P(vector) = i + 2j + 3k

                 Q(vector) = 3i + 5j + 7k

• Hence the vector PQ will be:

                 Q(vector) - P(vector) = 2i + 3j + 4k

• Now we have givn the force field:

                 F = x^3i + yj + zk

• So work done will be:

                 F.PQ = x^3i + yj + zk . 2i + 3j + 4k

                          = 2x^3 + 3y + 4z

Answer:

        So the work done by f along the line from points (1, 2, 3) to (3, 5, 7) is  2x^3 + 3y + 4z