Find a Unit Vector Orthogonal to Both of the Vectors $\{ 1 , - 1,0 \}$

question 116

Multiple Choice

Find a unit vector orthogonal to both of the vectors $\{ 1 , - 1,0 \}$ and $\{ 1,2,3 \}$ .

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

---

Definitions:

Hardy Personality

A personality trait characterized by resilience and the ability to cope effectively with stress.

Qualities

Characteristics or attributes that can be used to describe or evaluate something or someone.

Social Readjustment Rating Scale

A scale that measures the stressfulness of life events to predict the impact of stress on health.

Major Life Changes

Significant events or transitions in an individual's life that can have profound psychological and emotional impact, such as marriage, divorce, or loss of a loved one.