A, B, C, D, E, F in that order, are the ...

A, B, C, D, E, F in that order, are the vertices of a regular hexagon with centre orgin. If the position vectors of the vertices A and B are respectively, `4hati+3hatj-hatk and -3hati+hatj+hatk`, then DE is equal to

A

`7hati+2hatj-2hatk`

B

`-7hati-2hatj+2hatk`

C

`3hati-hatj-hatk`

D

`-4hati-3hatj+2hatk`

Text Solution

Verified by Experts

The correct Answer is:

A

Given, `OA=4hati+3hatj-hatk`
`OB=-3hati+hatj+hatk`
Now, `AB=OB-OA=-7hati-2hatj+2hatk`
`therefore DE=-AB=7hati+2hatj-2hatk`

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