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Assertion A : If A, B, C, D are four poi...

Assertion A : If A, B, C, D are four points on a semi-circular arc with centre at 'O' such that
`|vec(AB)| = |vec(BC)|=|vec(CD)|`, then
`vec(AB) +vec(AC) +vec(AD) =4 vec(AO) +vec(OB) +vec(OC)`
Reason R : Polygon law of vector addition yields
`vec(AB) +vec(BC) +vec(CD) +vec(AD)=2vec(AO)`

In the light of the above statements, choose the most appropriate answer from the options given below :

A

If both assertion and reason are true and the reason is the correct explanation of the assertion

B

If both assertion and reason are true but reason is not the correct explanation of the assertion

C

If assertion is true but reason is false

D

If the assertion and reason both are false

Text Solution

Verified by Experts

The correct Answer is:
B
`vec(OA) + vec(AB) = vec(OB)` ...(i)
`vec(OB) + vec(BC) = vec(OC)` ...(ii)
`vec(OC) + vec(CD) = vec(OD)` ...(iii)
`vec(AB) = vec(OB)- vec(OA)`
`vec(AC)= vec(OC)- vec(OA)`
`vec(AD) = vec(OD)- vec(OA)= -vec(OA)- vec(OA)`
`vec(AB) + vec(AC) + vec(AD) = vec(OB) + vec(OC) - vec(4OA)`
`=4 vec(AO) + vec(OB) + vec(OC)` ...(Assertion)
`vec(AB) + vec(BC) + vec(CD) = vec(OB) + vec(OC) + vec(OD)- vec(OA) - vec(OB)- vec(OC)`
`= - vec(OA) - vec(OA)= -2 vec(OA)`
`= 2 vec(AO)` ...(Reason)
Both Assertion and Reason are correct but reason is not the correct explanation of Assertion.
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