Question

Find the circulation of Bold Upper F equals 5 x Bold i plus 7 z Bold j plus 6 y Bold k around the closed path consisting of the following three curves traversed in the direction of increasing t.

Answer 1

The circulation of the given vector is (5/2)x² + 7yz + 6yz + C

Explanation:

Given that F = 5xi + 7zj + 6yk

The circulation of F is given as

Integral of F.dr

dr = idx + jdy + kdz

F.dr = (5xi + 7zj + 6yk).(idx + jdy + kdz)

= 5xdx + 7zdy + 6ydz

Integral of F.dr = Integral of (5xdx + 7zdy + 6ydz)

= (5/2)x² + 7yz + 6yz + C