Suppose a Curve C Is Parameterized By $\vec { r } ( t )$

question 73

Essay

Suppose a curve C is parameterized by $\vec { r } ( t )$ with $a \leq t \leq b$ and suppose $\vec { F }$ is a vector field $\vec{F}(t)=\vec{r}(t) \times \vec{r}^{\prime}(t)$ for $a \leq t \leq b$ .Explain why $\int _ { C } \vec { F } \cdot d \vec { r } = 0$

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Definitions:

Labour Efficiency Variance

The discrepancy between the actual hours worked and the standard hours expected to produce a certain level of output.

Variable Overhead

Costs that change in proportion with production volume or business activity levels, such as utilities or raw materials.

Labour Rate Variance

Labour rate variance is the difference between the actual hourly wage paid to workers and the standard wage rate expected, indicating variations in labor cost.

Material Quantity Variance

The difference between the actual quantity of materials used in production and the expected quantity, multiplied by the standard cost per unit.