Find a Unit Vector That Has the Same Direction as the Vector

question 249

Multiple Choice

Find a unit vector that has the same direction as the vector from the point P $( 1 , - 1,1 )$ to the point Q $( 3,2 , - 5 )$ .

• A) \(\left( - \frac { 1 } { 2 } , \frac { 1 } { 3 } , - \frac { 1 } { 6 } \right)\)
• B) \(\left\langle \frac { 1 } { 2 } , \frac { 1 } { 3 } , \frac { 1 } { 6 } \right\rangle\)
• C) \(\left\langle \frac { 7 } { 2 } , \frac { 7 } { 3 } , \frac { 7 } { 6 } \right\rangle\)
• D) \(\left\langle \frac { 2 } { 7 } , \frac { 3 } { 7 } , \frac { 6 } { 7 } \right\rangle\)
• E) \(\left\langle \frac { 1 } { 3 } , \frac { 1 } { 4 } , \frac { 1 } { 5 } \right\rangle\)
• F) \(\left( \frac { 2 } { 7 } , \frac { 3 } { 7 } , - \frac { 6 } { 7 } \right)\)
• G) \(\left( \frac { 2 } { 3 } , - \frac { 3 } { 4 } , \frac { 5 } { 6 } \right)\)
• H) \(\left( \frac { 2 } { 3 } , \frac { 3 } { 4 } , - \frac { 5 } { 6 } \right)\)

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Definitions:

Adaptive Value

The extent to which a trait, behavior, or characteristic increases the survival and reproductive success of an organism in its environment.

Mechanistic Causes

Explanations based on the physical and biochemical processes underlying phenomena, often used in scientific contexts to understand biological functions.

Darwinian Puzzle

A phenomenon or trait that appears to reduce the fitness of individuals, posing a question as to why it has evolved or been maintained through natural selection.

Chemicals

Substances with distinct molecular compositions that are used in or produced by chemical processes.