Given That $\overrightarrow { \mathbf { A } } + 2 \overrightarrow { \mathbf { B } } = x _ { 1 } \hat { \mathbf { i } } + y _ { 1 } \hat { \mathbf { j } }$

question 56

Multiple Choice

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

• A) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 5 } \left( x _ { 1 } + 2 x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 5 } \left( y _ { 1 } + 2 y _ { 2 } \right) \hat { \mathbf { j } }\)
• B) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 5 } \left( x _ { 1 } - 2 x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 5 } \left( y _ { 1 } - 2 y _ { 2 } \right) \hat { \mathbf { j } }\)
• C) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 5 } \left( x _ { 1 } + 4 x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 5 } \left( y _ { 1 } + 2 y _ { 2 } \right) \hat { \mathbf { j } }\)
• D) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 5 } \left( x _ { 1 } + 4 x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 5 } \left( y _ { 1 } + 4 y _ { 2 } \right) \hat { \mathbf { j } }\)
• E) \(\overrightarrow { \mathbf { A } } = \frac { 1 } { 5 } \left( x _ { 1 } + 4 x _ { 2 } \right) \hat { \mathbf { i } } + \frac { 1 } { 5 } \left( y _ { 1 } - 4 y _ { 2 } \right) \hat { \mathbf { j } }\)

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