Let $ { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }$ be a constant vector field and S be an oriented surface.
Show that $\int _ { S } \vec { F } \cdot \vec { d A } \leq \left( \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } \right) ( \text { Area of } S )$

Question

Let $  { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }$ be a constant vector field and S be an oriented surface.
Show that $\int _ { S } \vec { F } \cdot \vec  { d A } \leq \left( \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } \right) ( \text { Area of } S )$

Quizplus · Accepted Answer

The Answer of Let $  { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }$ be a constant vector field and S be an oriented surface.
Show that $\int _ { S } \vec { F } \cdot \vec  { d A } \leq \left( \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } \right) ( \text { Area of } S )$

Let F⃗=ai⃗+bj⃗+ck⃗ { \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }F=ai+bj​+ck

Let ${ \vec { F } } = a \vec { i } + b \vec { j } + c \vec { k }$