Given That $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$

question 50

Multiple Choice

Given that $\overrightarrow { \mathbf { A } } + \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$ and $\overrightarrow { \mathbf { A } } - \overrightarrow { \mathbf { B } } = x _ { 2 } \hat { \mathbf { i } } + y _ { 2 } \hat { \mathbf { j } }$ ,what is $\overrightarrow { \mathrm { A } }$ ?

• A) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } - x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } - y _ { 2 } \right) \hat { \mathbf { j } }\)
• B) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } - y _ { 2 } \right) \hat { \mathbf { j } }\)
• C) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } - x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } + y _ { 2 } \right) \hat { \mathbf { j } }\)
• D) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 2 } \left( y _ { 1 } + y _ { 2 } \right) \hat { \mathbf { j } }\)
• E) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 2 } \left( x _ { 1 } + x _ { 2 } \right) \hat { \mathbf { i } }\)

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Definitions:

Violent Behavior

Acts that involve physical force intended to hurt, damage, or kill someone or something.

Authoritarian

Refers to a governing system in which power is concentrated in the hands of a leader or a small elite not constitutionally responsible to the people.

Conscientious

Characterized by the desire to do one's work or duty well and thoroughly.

Obedient

Showing readiness to follow commands or guidance from others; complying with or conforming to a command or authority.