Given That $\vec { v }$ And $\vec { w }$ Are Non-Zero Vectors and That

question 37

Multiple Choice

Given that $\vec { v }$ and $\vec { w }$ are non-zero vectors and that $\vec { v } \cdot \vec { w } = 0$ and $\vec { v } \times \vec { w } = \vec { i } + \vec { j } + \vec { k }$ , then which of the following MUST be true? Select all that apply.

• A) \(\vec { v }\) is perpendicular to \(\vec { w }\) .
• B) \(\vec { v }\) is parallel or anti-parallel to \(\vec { w }\) .
• C)The angle \(\theta\) between \(\vec { v }\) and \(\vec { w }\) satisfies .
• D)The angle \(\theta\) between \(\vec { v }\) and \(\vec { w }\) satisfies .
• E)At least one of \(\| \vec { v } \|\) and \(\| \vec { w } \|\) is greater than 1.

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Definitions:

Limbic System

A complex system of nerves and networks in the brain, involved with instinct and mood, controlling basic emotions, and drives such as fear and pleasure.

Basic Survival Instincts

The innate, automatic behaviors and responses aimed at preserving one’s life and well-being.

Voluntary Movements

Movements controlled consciously by the brain, usually in response to stimuli or as deliberate actions, contrasting with involuntary movements like reflexes.

Cranial Nerves

are the twelve pairs of nerves that emerge directly from the brain, not the spinal cord, and control various functions of the body and head.