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The five sides of a regular pentagon are...

The five sides of a regular pentagon are represented by vectors `vec(A)_(1), vec(A)_(2), vec(A)_(3), vec(A)_(4)` and `vec(A)_(5)` in cyclic order as shown. Corresponding vertices are represented by `vec(B)_(1), vec(B)_(2), vec(B)_(3), vec(B)_(4) and vec(B)_(5)` drawn from the centre of the pentagon. Then, `vec(B)_(2) + vec(B)_(3) + vec(B)_(4) + vec(B)_(5)`=

A

`vec(A)_(1)`

B

`- vec(A)_(1)`

C

`vec(B)_(1)`

D

`- vec(B)_(1)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, `vec(B)_(1) + vec(B)_(2) + vec(B)_(3) + vec(B)_(4) + vec(B)_(5)= 0`
This is because of regular pentagon Hence, `vec(B)_(2) + vec(B)_(3) + vec(B)_(4) + vec(B)_(5)= - vec(B)_(1)`
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