Show That $\int _ { C } 2 x d x + 2 y d y + 2 z d z = \mathbf { a } \cdot \mathbf { a }$

question 15

Essay

Show that $\int _ { C } 2 x d x + 2 y d y + 2 z d z = \mathbf { a } \cdot \mathbf { a }$ , where $\mathbf { a } = a _ { 1 } \mathbf { i } + a _ { 2 } \mathbf { j } + a _ { 3 } \mathbf { k }$ , and C is any path from $( 0,0,0 )$ to $\left( a _ { 1 } , a _ { 2 } , a _ { 3 } \right)$ .

---

Definitions:

Tibialis Anterior

A muscle in the lower leg that is involved in dorsiflexion and inversion of the foot.

Fibularis Brevis

A muscle located on the lateral part of the lower leg, involved in plantar flexion and eversion of the foot.

Extensor Digitorum Longus

A muscle in the leg that helps in extending the toes and dorsiflexing the foot.

Fibularis Longus

A muscle located on the lateral side of the lower leg, important for plantar flexion and eversion of the foot.