Are the Two Planes Parallel? Justify Your Answer

question 93

Short Answer

Are the two planes $\mathbf { r } _ { 1 } ( s , t ) = \langle 1 + s + t , s - t , 1 + 2 s \rangle \text { and } \mathbf { r } _ { 2 } ( s , t ) = \langle 2 + s + 2 t , 3 + t , s + 3 t \rangle$ parallel? Justify your answer.

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Definitions:

Systematic Desensitization

A behavioral therapy technique used to gradually reduce anxiety through controlled exposure to feared stimuli.

Cognitive Therapy

A type of psychotherapy that aims to change negative patterns of thinking or behavior to treat psychological disorders and improve mental health.

Psychoanalysis

A therapeutic approach and theory of psychological disorders that emphasizes the role of unconscious factors in determining behavior, founded by Sigmund Freud.

Undesirable Behavior

Actions or conduct that are considered inappropriate, unacceptable, or harmful in a given context or society.