taiwan-gsat 2021 QC

taiwan-gsat · Other · ast__math-a 6 marks Vectors Introduction & 2D Expressing a Vector as a Linear Combination

Consider a trapezoid $ABCD$ where $\overline { AB }$ is parallel to $\overline { DC }$ . It is known that points $E$ and $F$ lie on diagonals $\overline { AC }$ and $\overline { BD }$ respectively, and $\overline { AB } = \frac { 2 } { 5 } \overline { DC }$ , $\overline { AE } = \frac { 3 } { 2 } \overline { EC }$ , $\overline { BF } = \frac { 2 } { 3 } \overline { FD }$ . If vector $\overrightarrow { FE }$ is expressed as $\alpha \overrightarrow { AC } + \beta \overrightarrow { AD }$ , then the real numbers $\alpha = \frac { \text{(16)} } { \text{(17)(18)} } , \beta = \frac { \text{(19)(20)} } { \text{(21)(22)} }$ . (Express as fractions in lowest terms)

Consider a trapezoid $ABCD$ where $\overline { AB }$ is parallel to $\overline { DC }$ . It is known that points $E$ and $F$ lie on diagonals $\overline { AC }$ and $\overline { BD }$ respectively, and $\overline { AB } = \frac { 2 } { 5 } \overline { DC }$ , $\overline { AE } = \frac { 3 } { 2 } \overline { EC }$ , $\overline { BF } = \frac { 2 } { 3 } \overline { FD }$ .\\
If vector $\overrightarrow { FE }$ is expressed as $\alpha \overrightarrow { AC } + \beta \overrightarrow { AD }$ , then the real numbers $\alpha = \frac { \text{(16)} } { \text{(17)(18)} } , \beta = \frac { \text{(19)(20)} } { \text{(21)(22)} }$ .\\
(Express as fractions in lowest terms)

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