Find the Area of the Surface of the Portion of the Plane

question 103

Multiple Choice

Find the area of the surface of the portion of the plane $z = 3 - 6 x - 2 y$
in the first octant.

• A) \(\frac { 3 \sqrt { 3 } } { 8 }\)
• B) \(\frac { 3 \sqrt { 41 } } { 8 }\)
• C) \(\frac { 3 \sqrt { 6 } } { 8 }\)
• D) \(\frac { 8 \sqrt { 41 } } { 3 }\)
• E) \(\frac { 3 } { 8 \sqrt { 41 } }\)

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Definitions:

Perceptual Organization

The tendency to integrate perceptual elements into meaningful patterns.

Brightness Constancy

The tendency to perceive an object as being just as bright even though lighting conditions change its intensity.

Luminous

Emitting or reflecting light, brightly shining, often used to describe objects that can glow in the dark.

Law of Continuity

A principle in Gestalt psychology stating that elements that appear to follow in the same pathway tend to be grouped together perceptually.