a and b form the consecutive sides of a ...

a and b form the consecutive sides of a regular hexagon ABCDEF.

Text Solution

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The correct Answer is:

A, B

`AB=a,BC=b`
`thereforeAC=AB+BC=a+b` . . (i)
`AD=2BC=2b` . . (ii)
(because AD is parallel to BC and twice is length)
`CD=AD-AC=2b-(a+b)=b-a`
`FA=-CD=a-b` . . (iii)
`DE=-AB=-a` . . . (iv)
`EF=-BC=-b` . . (v)
`AE=AD+DE=2b-a` . . .(vi)
`CE=CD+DE=b-a-a=b-2a`. . . (vii).

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Consider the following If vec(a) and vec(b) are the vectors forming consecutive sides of a regular hexagon ABCDEF, then 1. vec(CE)=vec(b)-2vec(a) " " 2. vec(AE)=2vec(b)-vec(a) 3. vec(FA)=vec(a)-vec(b) Which of the above are correct?

1 and 2 only

2 and 3 only

1 and 3 only

1, 2, and 3

overline(a), overline(b) are vectors, overline(AB), overline(BC) determined by two adjacent sides of a regular hexagon ABCDEF.The vector represented by overline(EF) is

`overline(a)-overline(b)`

`overline(a)+overline(b)`

`2overline(a)`

`-overline(b)`

If a and b represent the sides vecAB and vecBC of a regular hexagon ABCDEF, then vecFA =

`b-a`

`a-b`

`a + b`

none of these