Question

Determine whether the line integral of each vector field (in blue) along the oriented path (in red) is positive, negative, or zero.

1) Positive
2) Negative
3) Zero

Answer 1

To determine whether the line integral of a vector field along an oriented path is positive, negative, or zero, you can use the right-hand rule. If the path passes through the point in the same direction as your extended thumb, the line integral is positive. If the path passes through the point in the opposite direction to your extended thumb, the line integral is negative. If the path does not pass through the point, the line integral is zero.

Step-by-step explanation:

To determine whether the line integral of a vector field along an oriented path is positive, negative, or zero, you can use the right-hand rule. Curl the fingers of your right hand in the direction of the path of integration. If the path passes through the point in the same direction as your extended thumb, the line integral is positive. If the path passes through the point in the opposite direction to your extended thumb, the line integral is negative. If the path does not pass through the point, the line integral is zero.