If a- b represent A B- B C respectively of a regular hexagon ABCDEF then C D- D E- E F- F A areA- b-a-a-b- a-bB- A-b- a- b- b-aC- b-a- a- b- a-bD- A - b - a - b - b - a

The correct option is A b a, a, b, a bABCDEF is a regular hexagon ⇒A⃗D=2B⃗C, E⃗D=A⃗B, F⃗E=B⃗C, F⃗A=D⃗C Given A⃗B=a, B⃗C=b Now A⃗B+B⃗C+C⃗D =A⃗D ⇒ a+b+C⃗D =2 B ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

If a, b repre...

Question

If a,b represent $- - \to A B, - - \to B C$ respectively of a regular hexagon ABCDEF then $- - \to C D, - - \to D E, - - \to E F, - - \to F A$ are

b-a, -a, -b, a-b

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A-b, a, b, b-a

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b-a, a, b, a-b

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A-b,-a,-b, b-a

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Solution

The correct option is A b-a, -a, -b, a-b
ABCDEF is a regular hexagon
$\Rightarrow \to A D = 2 \to B C, \to E D = \to A B, \to F E = \to B C, \to F A = \to D C$
Given $\to A B = a, \to B C = b$
Now $\to A B + \to B C + \to C D = \to A D \Rightarrow a + b + \to C D = 2 \to B C$
$\Rightarrow \to C D = 2 b - (a + b) = b - a \to D E = \to B A = - \to A B = - a, \to E F = \to C B = - \to B C = - b \to F A = \to D C = - \to C D = - (b - a) = a - b$

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Similar questions

Q. If a,b represent

- - \to A B, - - \to B C

respectively of a regular hexagon ABCDEF then

- - \to C D, - - \to D E, - - \to E F, - - \to F A

are

Q. If

a

and

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represent the sides

- - \to A B

and

- - \to B C

OF regular hexagon ABCDEF than

- - \to F A

Q. If

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is a regular hexagon with

- - \to A B = \to a

and

- - \to B C = \to b

,
(where

| \to a | = | \to b |

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Q. If

\vec{a}, \vec{b}

are the vectors forming consecutive sides of a regular hexagon ABCDEF, then the vector representing side CD is
(a)

\vec{a} + \vec{b}

(b)

\vec{a} - \vec{b}

(c)

\vec{b} - \vec{a}

(d)

- (\vec{a} + \vec{b})

Q. In a regular hexagon ABCDEF, A

\vec{B}

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\vec{b} and \vec{C D} = \vec{c}

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\vec{a} + \vec{b} + \vec{c}

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If a,b represent −−→AB,−−→BC respectively of a regular hexagon ABCDEF then −−→CD,−−→DE,−−→EF,−−→FA are

If a,b represent $- - \to A B, - - \to B C$ respectively of a regular hexagon ABCDEF then $- - \to C D, - - \to D E, - - \to E F, - - \to F A$ are