ABCDEF is a regular hexagon- If -B- - and B-b- then the other sides are represented by the vectors

The correct option is D ĈD̂ =b̂ â ,D̂Ê= ̂â ,ÊF̂ = ̂b̂,F̂Â =â b̂ |a|=|b| A⃗D⃗||B⃗C⃗ So #160; A⃗D⃗=k b⃗ |A⃗D⃗|=2|b| k=2 A⃗D⃗ ...

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Quantitative Aptitude

Area Based Approach

ABCDEF is a r...

Question

$A B C D E F$ is a regular hexagon. If $^A B =^a$ and $^B C =^b$ then the other sides are represented by the vectors

^C D =^a -^b,^D E =^a,^E F =^b,^F A =^a +^b

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^C D =^a +^b,^D E =^b,^E F =^a,^F A =^b -^a

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^C D =^b -^a,^D E =^- a,^E F =^- b,^F A =^a -^b

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^C D = 2^b -^a,^D E =^- b,^E F =^- a,^F A =^a -^b

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Solution

The correct option is D $^C D =^b -^a,^D E =^- a,^E F =^- b,^F A =^a -^b$
$| a | = | b |$
$\to A D | | \to B C$
So $\to A D = k \to b$
$| \to A D | = 2 | b |$
$k = 2$
$\to A D = \to A B + \to B C + \to C D$
$2 \to b = \to a + \to b + \to c d$
$\to b - \to a = \to C D$
$\to D E = \to - A B$
$\to D E = - \to a$
$\to E F = \to - B C$
$\to E F = - \to b$
$\to - C D = \to F A$
$\to a - \to b = \to F A$

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ABCDEF is a regular hexagon. If ^AB=^a and ^BC=^b then the other sides are represented by the vectors

The correct option is D ^CD=^b−^a,^DE=^−a,^EF=^−b,^FA=^a−^b|a|=|b|→AD||→BCSo →AD=k→b|→AD|=2|b|k=2→AD=→AB+→BC+→CD2→b=→a+→b+→cd→b−→a=→CD→DE=→−AB→DE=−→a→EF=→−BC→EF=−→b→−CD=→FA→a−→b=→FA

$A B C D E F$ is a regular hexagon. If $^A B =^a$ and $^B C =^b$ then the other sides are represented by the vectors