Find the Distance Between the Planes $$5 x - 2 y + z - 4 = 0,5 x - 2 y + z + 6 = 0$$

question 40

Multiple Choice

Find the distance between the planes. $$5 x - 2 y + z - 4 = 0,5 x - 2 y + z + 6 = 0$$

• A) \(\frac { 1 } { 6 }\)
• B) \(\frac { 1 } { 3 } \sqrt { 30 }\)
• C) \(\frac { 5 \sqrt { 30 } } { 6 }\)
• D) \(\frac { 5 } { 6 }\)
• E) \(\sqrt { 30 }\)

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Definitions:

Cognitive

Relating to the mental processes of perception, memory, judgment, and reasoning, as opposed to emotional or volitional processes.

Behavioral

Pertaining to the actions or reactions of a person or animal in response to external or internal stimuli.

Psychodynamic

A psychological perspective that emphasizes the influence of the unconscious mind, internal conflicts, and childhood experiences on behavior.

Existential

Relating to existentialism, a philosophical theory that emphasizes individual freedom, choice, and meaning within an inherently meaningless universe.