Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$

question 184

Short Answer

Evaluate $\iint _ { S } \mathbf { F } \cdot d \mathbf { S }$ , where $\mathbf { F } ( x , y , z ) = \frac { x } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { i } + \frac { y } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { j } + \frac { z } { \left( x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \right) ^ { 3 / 2 } } \mathbf { k }$ and S is the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 9$ .

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Definitions:

Grouping

Grouping refers to the process of organizing objects, individuals, or ideas into categories or clusters for easier understanding or analysis.

Size Constancy

The perceptual phenomenon in which the size of an object is perceived to remain constant despite changes in its distance from the observer.

Binocular Disparity

The difference in images captured by the left and right eyes due to their slightly different positions, crucial for depth perception.

Depth Perception

The ability to perceive the visual world in three dimensions and to judge distances accurately.