Consider the Plane $\vec { r } ( s , t ) = ( 3 + s - 5 t ) \vec { i } + ( 5 - s + 5 t ) \vec { j } + ( 5 - 10 t + s ) \vec { k }$

question 11

Multiple Choice

Consider the plane $\vec { r } ( s , t ) = ( 3 + s - 5 t ) \vec { i } + ( 5 - s + 5 t ) \vec { j } + ( 5 - 10 t + s ) \vec { k }$ Find a normal vector to the plane.

• A) \(\frac { 1 } { \sqrt { 2 } } ( \vec { i } + \vec { k } )\)
• B) \(\frac { 1 } { \sqrt { 3 } } ( \vec { i } + \vec { j } - \vec { k } )\)
• C) \(\frac { 1 } { \sqrt { 2 } } ( \vec { i } + \vec { j } )\)
• D) \(\frac { 1 } { \sqrt { 3 } } ( \vec { i } + \vec { j } + \vec { k } )\)
• E) \(\frac { 1 } { \sqrt { 2 } } ( \vec { i } - \vec { j } )\)

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Definitions:

Formal Operations

The fourth and final stage of Jean Piaget's theory of cognitive development, characterized by the ability to think abstractly, reason logically, and manage hypothetical situations.

Cognitive Development

The process by which a child learns to reason, solve problems, and understand concepts throughout different stages of early life.

Group Discussions

A form of communicative interaction among a small group of individuals, focusing on a predefined subject, with the aim of sharing information, solving problems, or generating ideas.

Cognitive Development

The process of growth in intellectual abilities such as thinking, reasoning, and problem-solving.