Express the Vector as a Product of Its Length and Direction

question 169

Multiple Choice

Express the vector as a product of its length and direction.
- $$\frac { 1 } { \sqrt { 6 } } \mathbf { i } + \frac { 1 } { \sqrt { 3 } } \mathbf { j } - \frac { 1 } { \sqrt { 2 } } \mathbf { k }$$

• A) \(\frac { 1 } { 6 } \left( \frac { 6 } { \sqrt { 6 } } \mathbf { i } + \frac { 6 } { \sqrt { 3 } } \mathbf { j } - \frac { 6 } { \sqrt { 2 } } \mathbf { k } \right)\)
• B) \(1 \left( \frac { 1 } { \sqrt { 6 } } \mathbf { i } + \frac { 1 } { \sqrt { 3 } } \mathbf { j } - \frac { 1 } { \sqrt { 2 } } \mathbf { k } \right)\)
• C) \(\frac { 1 } { 2 } \left( \frac { 1 } { 3 } \mathbf { i } + \frac { 2 } { \sqrt { 3 } } \mathbf { j } - \frac { 2 } { \sqrt { 2 } } \mathbf { k } \right)\)
• D) \(\frac { 2 } { 3 } \left( \frac { 3 } { 2 \sqrt { 6 } } \mathrm { i } + \frac { 3 } { 2 \sqrt { 3 } } \mathrm { j } - \frac { 3 } { 2 \sqrt { 2 } } \mathbf { k } \right)\)

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Definitions:

Peyer's Patches

Specialized lymphoid nodules located in the wall of the small intestine, playing a key role in immune responses against ingested substances.

Lymph Nodules

Lymph nodules are small, localized clusters of dense tissue found within the lymph system, important for immune responses and filtration of bodily fluids.

Small Intestinal Wall

The layered structure of the small intestine, consisting of mucosa, submucosa, muscularis, and serosa, facilitating nutrient absorption.

Cell-mediated Immunity

An immune response that does not involve antibodies but instead involves the activation of phagocytes, antigen-specific cytotoxic T-lymphocytes, and the release of various cytokines in response to an antigen.