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

question 73

Multiple Choice

Find a unit vector that has the same direction as the vector $\langle 1,1,1 \rangle$ .

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

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Definitions:

Marginal Cost

The increase in total production costs resulting from the production of one additional unit of a product or service.

Artificially Scarce Good

A product or service that is made scarce through artificial means such as monopoly control or government regulations, rather than limited by natural resources.

Externalities

Costs or benefits arising from an economic activity that affect third parties who did not choose to incur that cost or benefit.

Socially Optimal

A condition where resources are allocated in the most efficient way from the society's point of view, maximizing overall welfare.