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Q.

Let ABCD be a quadrilateral . If E and F are the mid points of the diagonal AC and BD respectively and $(\bar{AB} - \bar{BC}) + (\bar{AD} - \bar{DC}) = k \bar{FE}$ then k =

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a

-4

b

2

c

-2

d

4

answer is A.

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Detailed Solution

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$\bar{E} = \frac{\bar{a} + \bar{c}}{2} \bar{F} = \frac{\bar{b} + \bar{d}}{2} (\bar{AB} - \bar{BC}) + (\bar{AD} - \bar{DC}) = k \bar{FE} \Rightarrow (\bar{b} - \bar{a} - \bar{c} + \bar{b}) + (\bar{d} - \bar{a} - \bar{c} + \bar{b}) = k (\frac{\bar{a} + \bar{c}}{2} - \frac{\bar{b} + \bar{d}}{2}) \Rightarrow - 2 ((\bar{a} + \bar{c}) - (\bar{b} + \bar{d})) = k (\frac{\bar{a} + \bar{c}}{2} - \frac{\bar{b} + \bar{d}}{2})$
K = -4

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