At What Point on the Curve $x = t ^ { 3 } , y = 9 t , z = t ^ { 4 }$

question 131

Multiple Choice

At what point on the curve $x = t ^ { 3 } , y = 9 t , z = t ^ { 4 }$ is the normal plane parallel to the plane $3 x + 9 y - 4 z = 8 ?$
Select the correct answer.

• A) \(( - 9,1,1 )\)
• B) \(( - 1 , - 9,1 )\)
• C) \(( 9,18 , - 2 )\)
• D) \(( - 18,9,1 )\)
• E) \(( - 1 , - 3,9 )\)

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Definitions:

Intuitive Thinking

A cognitive process that involves making decisions or solving problems based on feelings, instincts, or perceptions without the use of rational processes.

Flexible

The ability to adapt or be adapted to changes, challenges, or varying needs with ease.

Spontaneous

Occurring naturally or without premeditation; impulsive and unrestrained.

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This term might not correspond to a widely recognized concept in psychology or management sciences in a direct manner, it might be a confusion or mixing of the terms used in psychological type theories.